HANDBOOKSfor  Students  andGcneml  Readers 


UC-NRLF 


Ifi?    200 


PRACTICAL  PHYSICS 


GUTHR1E 


LIBRARY  OF  THE  UNIVERSITY  OF  CALIFORNIA. 


Miss  ROSE  WHITING. 


September,  1896. 
Accession  No.  fa  3  &  7 &~       Oa*s  No. 


HANDBOOKS  for  Students  and  General  Readers 
IN  SCIENCE,  LITERATURE,  ART,  AND  HISTORY. 


Messrs.  HENRY  HOLT  &  Co.  have  begun  the  publication  of  a  Series  of 
brief  Handbooks  in  various  departments  of  knowledge.  The  grade  of  the 
books  is  intermediate  between  the  so-called  "pr  mers  "  and  the  larger  works 
professing  to  present  quite  detailed  views.  Generally,  they  will  be  found 
available  by  upper  classes  in  schools  which  can  not  give  much  time  to  the 
subjects,  and  by  mature  persons  of  little  leisure  who  wish  to  enlarge  or  revise 
their  knowledge. 

The  subjects  and  authors,  so  far  as  selected,  are  as  follows  : 

VOLUMES  PUBLISHED. 

Zoology  of  the  Invertebrate  Animals.  By  ALEX.  MACALISTER, 
M.I).,  Professor  of  Zoology  and  Comparative  Anatomy  in  the  University 
of  Dublin.  Specially  revised  tor  America  by  A.  S.  PACKARD.  JR., 
M  D.,  Professor  of  Zoology  and  Geology  in  Brown  University.  60  cts. 
This  and  the  following  together  in  one  vol.,  $1.00. 

Zoology  of  the  Vertebrate  Animals.  By  the  above  authors. 
i6mo.  60  cents.  This  and  the  preceding  together  in  one  vol.,  $1.00. 

Zoology.     The  preceding  two  volumes  in  one,  T6mo,  $1.00. 

The  Studio  Arts,     By  ELIZABETH  WINTHROP  JOHNSON.     i6mo.    6oc. 

Astronomy.  By  R.  S.  BALL,  LL.D.,  F.R.S..  Astronomer  Royal  lor 
Ireland.  Specially  Revised  for  America  by  SIMOX  NEWCOMB.  Superin- 
tendent American  Nautical  Almanac ;  formerly  Professor  at  the  U.  S. 
Naval  Observatory.  i6mo.  6oc. 

Practical  Physics— Molecular  Physics  and  Sound.  By 
FREDERICK  GUTHRIE,  PH.D.  F.R.SS.  L.  &  E.,  Professor  of  Physics  in 
the  Royal  Schojl  of  Mines,  London.  i6mo.  6oc.  (See  Practical 
Physics  below.) 

FORTHCOMING    VOL  UMES. 

Architecture.  By  RUSSELL  STURGIS,  A.M.,  Architect,  Professor  of 
Architecture  and  the  Arts  of  Design,  in  the  College  of  the  City  of  N.  Y. 

Botany.  Morphology  and  Physiology.  By  W.  R.  McNAB, 
M  D.,  F.L.S.,  Professor  of  Botany,  Royal  College  of  Science  for 
Ireland,  Dublin.  Revised  by  C.  E.  BESSEY,  M.S.,  Professor  of 
Botany  in  the  Iowa  Agricultural  College. 

Botany.     Classification  of  Plants.    By  W.  R.  McNAB.    Revised 

by  C.  E.  BKSSEY. 
English  Language.     By  T.  R.  LOUNSBURY,  Professor  in  Yale  College. 

English  Literature.    By  

French   Literature.     By  FERDINAND  BOCHER,  Professor  in  Harvard 

University. 

German  Literature.    By 

History  of  American  Politics.     By  ALEXANDER  JOHNSTON,  A.M. 
Jurisprudence.      By   JOHNSON  T.    PLATT,    Professor    in    the    Law 

Department  of  Yale  College. 

Practical     Physics— Electricity     and     Magnetism.       By 

Prof.  F.  GUTHRIE,  Ph.D. 
Practical  Physics— Heat  and  Light.     By  Prof.   F.    GUTHRIE, 

Physical  Geography.  By  CLARENCE  KING,  Director  of  the  U.  S. 
Government  Surveys. 

Political  Economy.  By  FRANCIS  A.  WALKER,  Ph.D.,  Professor  in 
Yale  College. 


HANDBOOKS  for  Students  and  General  Readers 


PRACTICAL     PHYSICS 


MOLECULAR  PHYSICS  6*  SOUND 


BY 


FREDERICK  GUTHRIE,  PH.D.  F.R.SS.  L.  &  E. 

PROFESSOR   OF   PHYSICS 
IN  THE  ROYAL  SCHOOL  OF  MINES,   LONDON. 


NEW  YORK 

HENRY   HOLT   &   COMPANY 
1879 


EXPLANATORY. 


THIS  Series  is  intended  to  meet  the  requirement  of 
brief  text-books  both  for  schools  and  for  adult  readers 
who  wish  to  review  or  expand  their  knowledge. 

The  grade  of  the  books  is  intermediate  between  the 
so-called  "primers"  and  the  larger  works  professing 
to  present  quite  detailed  views  of  the  respective  sub- 
jects. 

Such  a  notion  as  a  person  beyond  childhood  re. 
quires  of  some  subjects,  it  is  difficult  and  perhaps 
impossible  to  convey  in  one  such  volume.  Therefore, 
occasionally  a  volume  is  given  to  each  of  the  main 
departments  into  which  a  subject  naturally  falls — for 
instance,  a  volume  to  the  Zoology  of  the  vertebrates, 
and  one  to  that  of  the  invertebrates.  While  this  ar- 
rangement supplies  a  compendious  treatment  for  those 
who  wish,  it  will  also  sometimes  enable  the  reader 
interested  in  only  a  portion  of  the  field  covered  by  a 
science,  to  study  the  part  he  is  interested  in,  without 
getting  a  book  covering  the  whole. 

Care  is  taken  to  bring  out  whatever  educational 
value  may  be  extracted  from  each  subject  without  im- 


vi  Explanatory. 

peding  the  exposition  of  it.  In  the  books  on  the 
sciences,  not  only  are  acquired  results  stated,  but  as 
full  explanation  as  possible  is  given  of  the  methods  of 
inquiry  and  reasoning  by  which  these  results  have 
been  obtained.  Consequently,  although  the  treatment 
of  each  subject  is  strictly  elementary,  the  fundamental 
facts  are  stated  and  discussed  with  the  fulness  needed 
to  place  their  scientific  significance  in  a  clear  light, 
and  to  show  the  relation  in  which  they  stand  to  the 
general  conclusions  of  science. 

Care  is  also  taken  that  each  book  admitted  to  the 
series  shall  either  be  the  work  of  a  recognized  author- 
ity, or  bear  the  unqualified  approval  of  such.  As  far 
as  practicable,  authors  are  selected  who  combine 
knowledge  of  their  subjects  with  experience  in  teach- 
ing them. 


AUTHOR'S  PREFACE. 


I  HOPE  that  the  following  outlines  of  Practical  Physics, 
including  Molecular  Physics,  Waves,  Sound,  Light  and 
Heat,  may  be  of  use  to  those  Teachers  and  Students 
who  wish  to  give  or  to  get  more  than  a  mere  word- 
knowledge  of  the  matter.  Such  knowledge  alone  no 
more  gives  its  owner  a  right  to  be  reckoned  a  Physicist 
than  does  a  knowledge  of  sound  and  harmony  entitle 
him  to  be  called  a  Musician,  or  a  knowledge  of  per- 
spective and  colour  to  the  name  of  Artist. 

It  has  been  the  strong  wish  and  effort  of  some  few 
Physicists  of  late  years  to  bring  practical  work  into 
their  teaching,  and  thus  to  do  for  Physics  what  has 
been  for  so  long  done  for  Chemistry  with  great  gain. 
For  it  seems  that  knowledge  got  by  the  head  alone 
is  often  very  fleeting  :  whereas  when  head  and  hand 
learn  together,  the  power  of  keeping  is  strengthened. 
And  we  look  upon  such  practical  teaching  as  good, 
not  only  because  it  is  the  only  way  to  forge  the  link 
by  which  man  is  bound  to  nature,  but  also  because 
it  forms  the  one  discipline  of  truth  in  the  ways  of 

matter. 

FREDERICK  GUTHRIE. 
LONDON,  1878. 


CONTENTS. 


COHESION  OF  SOLIDS. 

SUCTION  PAOB 

1-7.     Hardness.  —  Form-Elasticity.  —  Tenacity.  — 

Torsion .1-8 


COHESION  OF  LIQUIDS  AND  GASES. 

8-19.    Jets.  —  Rupture. — Drop  size.  —  Bubble  size.  — 

Viscosity 8-19 


VOLUME-ELASTICITY  OF  SOLIDS,  LIQUIDS, 
AND  GASES. 

20-23.     Elasticity  of  Liquids. — Elasticity  of  Gases. — 

Relation  between  volume  and  pressure.          19-23 


COHESION  OF  LIQUIDS  AFFECTED  BY 
ADHESION  TO  SOLIDS. 

24-29.     Capillarity 23-28 


COHESION  OF  SOLIDS  AFFECTED  BY  ADHESION 
TO  LIQUIDS.— ABSORPTION  OF  GASES.— DIF- 
FUSION. 

30-59.     Solution.— Diffusion   of  liquids  into  liquids. — 
Diffusion  of  gases  into  liquids. — Absorption.— 


Contents. 


PACK 

Occlusion.  —  Breath  pictures.  —  Diffusion  of 
gases  into  gases. — Effusion. — Diffusion  of 
liquids  into  gases. — Vapour  tension. — Dif- 
fusion of  liquids  into  solids. — Osmose. — 
Dialysis.— Transpiration  .  .  .  29  54 


DENSITY.— SPECIFIC  GRA  VITY. 

60-73.     Of  Solids.  —Liquids.  — Solids  lighter  than  water. 

Solids  soluble  in  water.         .        .        .        55-63 


VORTEX  MOTION. 
74.     Vortex  motion  in  gases  and  liquids.  .        63-65 

WA  VES. 

75-83.  Water  waves.  — Reflexion  of  water  waves. — 
Stationary  water  waves.  —  Waves  governed 
by  elasticity. — Notes. — Detection  of  sound.— 
Sensitive  flame. — Reflexion  of  sound. — Ab- 
sorption of  sound. — Refraction  of  sound. — 
Dispersion  of  sound 65-82 

ORIGINS  OF  SOUND    WAVES. 

84-95.  Transverse  vibrations  of  rods. —Composition  of 
vibrations. — Transverse  waves  in  strings. — 
Nodes,— Stationary  waves. — Vibrating  strings 
as  sources  of  sound. — Musical  scale. — Nodes 
in  rods. — The  bell. — Thunder. — Nodes  and 
segments  of  vibrating  plates.  .  .  83-104 

THE  GAS  WAVE. 

96-99.      Vibrations  in  gases— Closed  and  open  tubes. 

— Nodes  in  open  tubes. — Resonance     .    104-112 


Contents.  xi 


LONGITUDINAL    VIBRATIONS  IN  LIQUIDS 
AND  SOLIDS. 

SECTION  PAGB 

loo-iio.  Transmission  of  sound. — The  string  telephone. 
Interference. — Beats. — Singing  flames. — Si- 
nuosities.— Effect  of  motion  of  source  of  sound. 
— Sympathy.  —  Approach  caused  by  vibra- 
tion.— The  phonograph.  .  .  .112-124 


APPENDIX. 

111-115.  The  vernier. — Parchment  paper. — Hints  on 
glass  working. — To  etch  a  scale  on  glass. — 
The  siphon  barometer.  .  .  .  125-133 

ELEMENTARY  EXPERIMENTS   RELATING    TO 

SOUND  AND    WAVES         ....     134-150 


APPARATUS    AND    MATERIAL    FOR    EXPERI- 
MENTS IN  SOUND  AND   WAVES  .         .     151-154 


INDEX 


PRACTICAL    PHYSICS. 

PART   I. 

MOLECULAR  PHYSICS  AND  SOUND. 

COHESION   OF  SOLIDS. 

§  i.  Hardness.  Form-elasticity. — The  pressure 
required  to  alter  the  relative  positions  of  two  contiguous 
parts  of  a  body  measures  its  hardness.  As  this  pressure 
is  greater  with  greater  surfaces  of  contact,  some  unit  of 
surface  must  be  fixed  upon.  The  term  hardness  is 
generally  applied  loosely  to  difficulty  of  fracture.  The 
following  remarks  may  show  that  our  speech  and  ideas 
in  regard  to  hardness  are  deficient  in  precision.  Glass 
is  said  to  be  harder  than  lead,  yet  a  glass  cup  is  more 
easily  broken  than  a  leaden  one — more  easily  broken, 
though  not  so  easily  bent.  Hard  bodies  are  always 
elastic ;  elastic  bodies  are  not  necessarily  hard,  nor  are 
they  necessarily  brittle,  nor  are  soft  bodies  necessarily 
plastic.  Toughness  seems  to  imply  a  resistance  to 
change  of  form,  which  resistance  increases  more  rapidly 
than  the  displacement;  thus,  while  a  band  of  vulcanised 
caoutchouc  will  be  extended  to  a  degree  proportional 
to  the  weight  hung  at  one  end,  a  leathern  strap  will 


2  Practical  Physics. 

not  be  extended  twice  as  far  if  the  weight  on  it  is 
doubled.  Toughness  is  generally  associated  with 
texture,  and  stretching  causes  partial  fibration  in  the 
line  of  pull. 

The  hardness  of  minerals,  stones,  and  similar 
bodies,  is  usually  referred  to  the  terms  of  the  follow- 
ing series : 

(1)  Talc          .         .         .     Silicate  of  magnesium 

(2)  Gypsum  (selenite)      .     Sulphate  of  calcium 
($)  Rock  salt .         .         .     Chloride  of  sodium 

(4)  Calc-spar  .         .         .     Carbonate  of  calcium 

(5)  Apatite     .         .         .     Phosphate  of  calcium 

(6)  Felspar     .        .         .     Silicate     of     potassium 

and  aluminum 

(7)  Quartz      .         .         .     Silica 

(8)  Topaz      .         .        .     Fluosilicate  of  aluminum 

(9)  Corundum  (sapphire, 

ruby)     .         .        .    Alumina 
(ro)  Diamond  .         .        .     Crystallised  carbon 

Each  of  these  scratches  all  of  those  above  it,  and  is 
scratched  by  those  below.  Thus,  if  a  body  under  exa- 
mination is  found  to  scratch  felspar,  but  to  be  scratched 
by  quartz,  its  hardness  is  said  to  be  between  6  and  7. 
This  method  of  comparison  is  somewhat  vague  ;  it  is 
usually  applied  by  rubbing  an  edge  or  point  of  one 
body  on  a  surface  of  the  other,  and  although  of  course 
the  common  surface  of  the  two  is  identical,  the  sur- 
faces are  not  equally  supported  by  surrounding  matter. 
On  rubbing  together  two  equal  spheres  of  iron  and 
lead,  the  latter  metal  is  rubbed  off ;  on  pressing  them 
together,  the  lead  is  indented,  showing  that  its  cohesion 


Hardness.     Tenacity.  3 

or  hardness  is  less  than  that  of  the  iron.  Nevertheless, 
a  leaden  bullet  will  pierce  an  iron  plate,  and  a  rapidly 
revolving  disc  of  iron  will  cut  the  hardest  steel.  Also 
if  a  glass  tube  be  broken  in  the  middle,  the  jagged 
edge  can  be  broken  off  by  the  smooth  tube,  and  the 
smooth  tube  can  be  scratched  by  the  ragged  edge. 

§  2.  The  cohesion  of  metals  is  usually  measured 
as  tenacity,  that  is,  by  finding  the  maximum  weight 
which  wires  of  a  given  thickness  will  carry.  The 
drawing  of  a  wire  through  a  stock  tends,  however,  to 
render  the  metal  fibrous,  and  to  give  it  a  skin  which 
is  more  tenacious  even  than  the  interior.  Since  the 
surface  varies  with  the  diameter,  and  the  sectional 
area  with  the  square  of  the  diameter,  two  wires,  each 
of  sectional  area  0,  will  support  more  than  one  of 
sectional  area  2 a,  because  the  sum  of  the  circum- 
ferences or  skin-rings  of  the  two  is  greater  than  the 
skin-ring  of  the  larger  wire.  Thus,  a  drawn  steel  rod 
of  i  meter  in  length  will  not  support  so  much  as  the 
same  steel  drawn  into  a  wire  1,000  meters  long,  cut 
up  into  1,000  lengths  of  i  meter  each,  and  forming  a 
bundle.  The  tenacity  of  the  skin  can  be  reduced  by 
annealing  (heating  and  slow  cooling),  but  it  is  here, 
as  always,  impossible  to  get  the  solid  body  perfectly 
homogeneous.  Some  experimental  measure  may  be 
got  of  the  tenacity,  by  fastening  one  end  of  the  wire 
to  a  spring  balance  rigidly  fixed  and  the  other  to  a 
pianoforte  peg,  and  turning  the  peg  till  the  wire 
breaks.  After  one  wire  has  been  broken,  a  second  is 
taken,  and  the  index  is  more  narrowly  watched,  or 
made  self-registering. 

§  3.  Wires  which  are  pulled  by  forces  insufficient 


4  Practical  Physics. 

to  break  them  are  elongated,  and  return  after  the 
withdrawal  of  the  stretching  force  more  or  less  com- 
pletely and  rapidly  (from  a  second  to  several  days)  to 
their  original  lengths.  To  prove  that  within  the  limits 
of  such  elasticity  the  extension  is  proportional  to  the 
stretching  force,  two  points  or  lines  are  marked  on 
the  wire,  which  should  for  this  purpose  be  two  or  three 
yards  long,  the  marks  being  an  inch  or  two  from  each 
end.  The  wire  is  hung  vertically,  is  gently  weighted, 
and  while  so  strained  it  is  annealed  by  passing  along 
fc  the  flame  of  an  air-gas  burner.  If  the  metal  will 
bear  it,  each  part  is  made  red-hot  in  succession. 
This  removes  kinks,  and  makes  the  wire  absolutely 
straight.  The  distance  of  the  marks  apart  is  then 
measured  by  a  cathetometer,  and  the  distance  is  again 
measured  when  the  stretching  weight  is  changed.  It 
may  be  assumed  that  all  parts  of  the  wire  are  stretched 
equally  ;  it  may  also  be  assumed  that  the  volume  of 
the  metal  remains  approximately  unchanged,  so  that 
if  the  elongation  is  such  that  the  length  m  becomes  /z, 

the  original  diameter  d  becomes  d\/—.    Besides 

V     n 

this  true  elasticity,  whereby  wires  recover  their  length, 
they,  when  stretched  nearly  to  breaking,  become  per- 
manently elongated.  A  thin  copper  wire  may  be  cau- 
tiously stretched  between  the  hands  a  quarter  of  its 
length  longer,  and  every  wire  will  bear  more  if  loaded 
gradually  than  if  loaded  quickly,  even  though  the  latter 
operation  be  quite  continuous. 

§  4.  Elasticity. — Bodies  differ  from  one  another  in 
regard  to  elasticity  (i)  as  to  the  pressure  required  to 
produce  a  given  deformation,  and  (2)  as  to  the  reco- 


Form-elasticity.     Torsion.  5 

very  of  their  original  form  after  deformation.  Hard 
steel  and  glass,  for  example,  recover  their  form  very 
perfectly  even  after  great  deformation  ;  while  in  lead 
the  recovery  is  complete  only  when  the  deformation 
has  been  very  small.  The  pressure  necessary  to  cause 
and  maintain  a  given  deformation  may  be  called  degree 
of  elasticity.  Vulcanised  caoutchouc  is  nearly  perfectly 
elastic  for  small  displacements,  but  its  elasticity  is  not 
so  strong  as  that  of  glass,  steel,  or  ivory.  The  elas- 
ticities of  wires  and  rods  can  of  course  be  directly,  but 
only  roughly,  measured  by  the  elongation  method.  If 
a  rectangular  rod  be  bent  from  the  straight  to  an  arc,  the 
outer  face  is  elongated  and  the  inner  crushed  together, 
and  accordingly  there  is  a  certain  surface  which  is 
neither  stretched  nor  crushed.  When  a  rod  or  wire, 
which  may  be  supposed  to  be  vertical  and  fastened 
above,  is  twisted,  every  series  of  particles  which  to 
begin  with  lay  in  a  horizontal  plane  still  do  so,  but 
the  plane  itself  is  raised.  Particles  which  lay  in  a 
vertical  line  now  lie  in  a  spiral,  and  contiguous  ver- 
tical lines  of  particles  must  slide  over  one  another. 
The  rod  or  wire  shortens,  and  there  is  on  the  whole 
an  intermolecular  motion  proportional  to  the  pressure 
maintaining  the  twist  or  torsion.  And  this  fact  fur- 
nishes the  best  method  of  proving  that  with  the  same 
substance  the  elasticity,  or  effort  to  regain  original 
shape,  varies  with  the  angle  of  torsion  or  deformation. 
§  5.  A  horseshoe  magnet,  M,  is  set  up  under  a 
bell-jar  in  a  vertical  plane  (fig.  i).  Two  pieces  of 
cardboard  or  mica  are  stuck  on  the  poles  on  alternate 
sides.  Two  little  equal  soft-iron  bullets  are  soldered 
to  the  ends  of  a  stiff  brass  wire,  w3  which  is  then  bent 


6 


Practical  Physics. 


twice  at  right  angles  in  a  plane,  so  that  when  the 
centre  of  the  wire  is  in  the  axis  of  the  jar  the  bullets 
may  rest  on  the  cardboard.  One  end  of  the  wire 
which  is  being  experimented  on  is  soldered  to  the 
middle  of  the  brass  wire,  the  other  passes  through  a 
FlG.  x-  narrow  glass  tube,  /,  at  the  upper  end  of 
which  it  is  fastened  by  a  drop  of  sealing- 
wax.  The  tube  passes  stiffly  through  a 
cork  in  the  mouth  of  the  bell-jar  and 
carries  an  index,  which  passes  over  a 
scale  of  angles  on  the  cork.  A  horse- 
shoe keeper  is  placed  on  the  magnet,  and 
the  tube  is  turned  till  the  balls  are  in 
contact  with  the  cardboard.  The  keeper 
is  then  removed,  and  the  balls  are  at- 
tracted to  the  poles.  Gradually  turn  the 
tube  in  the  cork  till  separation  ensues  ;  read  off  the 
angle  of  torsion,  ol5  measure  the  length,  /,,  of  the 
wire  from  the  glass  tube  to  the  brass  wire.  Soften 
now  the  wax  which  holds  the  wire  in  the  tube  and 
alter  the  length  of  the  free  wire  to  /2,  pushing  the 
tube  through  the  cork  till  the  balls  rest  exactly  where 
they  did  before.  Turn  as  before  till  separation  ensues. 
The  new  angle  being  a2,  it  is  found  that 


l\  __ 


"2 


Or  if  the  wire  be  twice  as  long,  the  upper  end  must 
be  twisted  through  twice  the  angle  in  order  to  give  a 
given  thrust  at  the  lower  end.  One  may  derive  the 
same  fact  by  reasoning  only,  in  the  following  way. 
Suppose  a  pair  of  tangentially  acting  forces,  //, 


Torsion.     Torsion  Pendulum.  7 

applied  at  given  arms,  a  a,  to  the  middle  of  a  wire 
of  length  /,  fixed  at  the  top  but  hanging  free  below,  to 
cause  an  angular  twist  of  a  there,  and  therefore  also  at 
the  bottom  of  the  wire.  Clamp  the  wire  in  the  middle, 
and  the  frictional  resistance  of  the  clamp  will  perform 
the  same  office  as  the  pressures  fi  and  /.  Twist  now 
the  bottom  end  also  with  pressures/  and/,  also  acting 
at  arms  a  and  a.  They  will  turn  the  end  round  through 
an  angle  «,  and  if  the  clamp  be  now  loosened,  the  wire 
will  be  found  to  be  in  equilibrium.  So  that,  applied 
at  the  end,  a  pair  of  twisting  forces  (a  couple)  will 
give  a  torsion  angle  2 a  if  they  give  an  angle  a  when 
applied  in  the  middle 

FfG.    2. 

o 


§  6.  To  show  that,  with  the  same  length  of  wire, 
the  pressure  is  proportional  to  the  angular  displace- 
ment, the  wire  can  be  fastened  as  in  fig.  2.  Its  cross- 
arm  at  the  bottom  rests  against  the  two  vertical  arms 
of  two  balanced  levers  provided  with  scale-pans.  If 
the  upper  end  of  the  wire  receives  a  given  twist,  the 
lower  end  is  kept  in  its  place  by  altering  the  weights 
in  the  scale-pans.  With  double  the  twist  the  weights 
must  be  doubled,  and  so  on. 

§   7.   By  far   the  best  proof  of  this   relationship, 


8  Practical  PJiysics. 

although  an  indirect  one,  is  the  isochronism  of  a  tor- 
sion pendulum.  A  cannon-ball  is  bored  through  the 
middle ;  a  steel  wire  is  fastened  to  it  with  lead,  the 
other  end  being  supported  on  a  strong  stand ;  the  ball 
is  twisted  round  three  or  four  times,  and  let  go.  It  may 
keep  its  motion  forwards  and  backwards  for  forty-eight 
hours.  Whatever  may  be  its  angular  amplitude  of 
swing,  its  period  is  very  nearly  identical.  This  can 
only  be  the  case  if  the  angle  of  displacement  is  pro- 
portional to  the  pressure  of  displacement— a  condition 
approximately  fulfilled  by  the  common  pendulum  only 
when  the  arc  traversed  is  so  small  as  to  be  sensibly 
equal  to  the  corresponding  chord. 


COHESION  OF   LIQUIDS. 

§  8.  That  liquids  have  cohesion  is  shown  in  a 
variety  of  ways.  A  drop  of  water  on  a  board  strewn 
with  powdered  resin  is  nearly  spherical.  The  .smaller 
the  drop  the  more  nearly  spherical.  So  is  a  drop  of 
water  on  a  sheet  of  paraffin,  or  a  drop  of  mercury  upon 
almost  every  substance.  The  spherical  is  the  form  in 
which  the  mean  distance  of  all  parts  from  the  centre  of 
mass  is  the  least.  It  is  the  most  compact  form  for  a 
given  mass.  This  shows  that  cohesion  moulds  the  drop 
to  the  spherical  form.  This  result  is  very  elegantly 
shown  by  making  such  a  mixture  of  alcohol  and  water 
as  has  the  same  specific  gravity  as  olive  oil.  Alcohol 
being  lighter  and  water  heavier  than  oil,  alcohol  is 
added  to  water  in  which  there  are  a  few  drops  of  oil 


Liquid  Cohesion.     Jets.     Rupture.  9 

until  the  latter  just  float  when  the  mixture  has  cooled  to 
the  ordinary  temperature.  Fresh  oil  is  then,  by  means 
of  a  pipette,  poured  into  the  middle  of  the  mixture. 
Spherical  globes  several  inches  in  diameter  can  thus 
be  formed. 

§  9.  One  of  the  best,  as  it  is  one  of  the  simplest, 
methods  of  measuring  the  cohesion  of  liquids  is  to  sus- 
pend a  flat,  round  plate  of  glass,  thoroughly  cleaned, 
from  one  pan  of  a  balance,  and  to  counterpoise  it ; 
the  surface  of  the  glass  being  adjusted  so  as  to  be 
exactly  level,  bring  under  it  a  dish  of  water,  and  lift  and 
support  the  dish  till  the  bottom  of  the  plate  is  in  con- 
tact, without  air  bubbles,  with  the  water,  taking  care  not 
to  wee  the  top  ;  load  gradually  the  other  pan  till  the 
plate  is  torn  away.  It  does  not  matter  what  the  plate  is 
made  of,  provided  it  is  wet  by  water ;  the  same  force  is 
required,  and  this  is  the  force  required  to  tear  asunder 
a  given  surface  of  water  from  the  neighbouring  lower 
surface.  It  is  not  the  separation  of  water  from  glass, 
because  the  lower  surface  of  the  glass  remains  com- 
pletely wetted.  A  good  way  of  hanging  the  glass  is  to 
heat  it  and  fasten  by  wax  three  threads  to  its  upper 
surface.  These  are  tied  together  a  few  inches  above 
the  plate,  and  fastened  to  a  single  thread  which  is 
fastened  to  the  pan  of  a  balance.  On  wiping  the  glass 
dry  and  replacing  the  water  by  alcohol,  a  less  force  is 
found  to  be  necessary. 

§  10.  A  beautiful  way  of  showing  that  water  has 
cohesion  is  to  let  a  smooth  vertical  column  of  water, 
not  flowing  too  fast,  fall  fair  upon  a  small  round  cup 
or  horizontal  disc.  The  water  is  thrown  off  horizon- 
tally, but  is  not  scattered  as  spray;  it  draws  itself 


IO  Practical  Physics. 

together,  forming  a  sort  of  film  water-bottle  of  grace- 
ful form.     Mercury  acts  in  a  similar  manner. 

§11.  Another  method  of  showing  liquid  cohesion 
is  to  close  one  end  of  a  wide  glass  tube,  bend  it  in  the 
middle,  draw  out  the  other  end,  and  tie  over  it  a  piece 
of  black  caoutchouc  tubing.  The  tube  (fig.  3)  is 
nearly  filled  with  water,  which  is  then  boiled  uniformly 
till  about  a  quarter  has  been  boiled  off.  The  caout- 
chouc is  then  pinched  between  the  fingers  near  the 
glass,  and  the  flame  is  withdrawn.  In  a  few  seconds 
the  fingers  may  be  taken  away,  and  the  narrow  part  of 
the  neck  may  be  sealed  off  over  the  flame.  The 
pressure  of  the  air  closes-  the  caoutchouc,  and  assists 
the  closing  of  the  glass.  On  cautiously  turning  the 
FIG.  3.  tube  over,  the  liquid  stands  as 

in  the  figure.  Accordingly,  as 
the  water-column  does  not 
break,  it  must  have  cohesion.  A 
smart  rap  on  the  table  breaks 
the  column,  and  the  water  then  stands  at  the  same 
height  in  both  limbs. 

§  12.  The  cohesion  of  liquids   can  be  most  ac- 
curately measured  and  compared  by  determining  the 
degree  to  which  such  cohesion  has  affected  the  size  of 
afaikn  drop.     What  is  here  meant  by  a  drop  is  a 
FIG.  4.  mass  °f  liquid  (fig.  4)  which  has 

J~~~  |   wetted  a  solid  and  which  has  ac- 

^-— ^  AT     *Y\       cumulated  on  the  solid  until  its 
^       cohesion  has  been  overcome  by 
its   own  weight.      It  then   falls,  its  size   depending 
very  little  upon  the  nature  of  the  solid  from  which  it 
falls,  but  very  much  upon  the  rate  at  which  it  drops, 


Drop-size. 


il 


upon  the  shape  of  the  surface  from  which  it  drops, 
upon  the  density  of  the  liquid,  and  upon  its  cohesion. 
To  show  how  much  depends  upon  rate,  other  things 
being  the  same,  let  water  flow  from  a  siphon  provided 
with  a  stop-cock  upon  a  glass  sphere  (a  round  glass 
flask)  so  that  the  drops  succeed  one  another  at  the  rate 
of  2  per  second.  Catch  100  in  a  weighed  flask  and 
weigh.  Let  now  the  drops  succeed  one  another  at  the 
rate  of  i  in  10",  or  twenty  times  as  slow  as  before  ; 
catch  100  and  weigh.  The  first  hundred  will  weigh  far 
more  than  the  last :  about  one-third  as  much  again. 
And  of  course  every  drop  of  the  quick  delivery  bears 
this  proportion  to  every  drop  of  the  slow. 

§  13.  Again,  other  things  being  the  same,  the 
flatter  the  surface  the  larger  the  drop.  Fasten  (fig.  5) 
three  round  glass  flasks  one  above  the  othrr  in  order 
of  magnitude,  and  put  a  little  muslin 
cap  on  each.  Let  water  flow  ircm 
a  tube  upon  the  upper  one.  Droj  s 
will  fall  from  this  to  the  next  lower, 
from  this  to  the  third,  and  from  the 
third  into  a  basin.  The  same  quan- 
tity of  water  drops  in  the  same  time 
from  each  sphere,  or  if  anything  a 
little  less  from  the  lower  spheres  on 
account  of  evaporation.  And  ytt 
the  drops  succeed  one  another  far  faster  from  the 
lower  than  from  the  uppei  spheres.  The  largest 
drops  are  those  which  fall  from  a  flat  surface.  The 
effects  of  density  and  cohesion  are  opposed  to  each 
other,  but  experiment  shows  that  increase  in  specific 
gravity,  which  by  itself  always  tends  to  diminish  drop 


FIG.  5. 


12  Practical  Physics. 

size,  may  be  more  than  counterbalanced  by  increased 
cohesion.  Thus  if  the  radius  of  a  sphere  of  platinum 
be  i *i 4  centimeters,  and  various  liquids  be  made  to 
drop  from  it  at  the  rate  of  one  drop  in  every  2",  at  a 
temperature  of  26°  C.,  the  actual  volumes  in  cubic 
centimeters  of  i  drop  of  each  liquid  are  as  follows  : 

Water    .         .        .         .         .<  0-148 

Glycerine       .        .         .        .  0*103 

Mercury         .        .         .         .  0-058 

Benzol °'°55 

Oil  of  Turpentine  .         .        .  0*050 

Alcohol          ....  0*049 

(glacial)  Acetic  acid    .        .        .        .  0*043 

The  mercury  is  made  to  touch  the  platinum  by  rubbing 
the  surface  of  the  platinum  with  a  little  mercury  in 
which  a  minute  fragment  of  sodium  has  been  dissolved. 
The  sodium  is  rubbed  into  the  mercury  in  a  dry  por- 
celain mortar,  whereupon  the  two  unite  with  liberation 
of  heat.  The  platinum  is  then  washed  in  fresh  clean 
mercury. 

Constancy  in  delivery  is  got  by  using  a  siphon  and 
inverting  into  the  basin  which  feeds  the  siphon  a  flask 
containing  the  same  liquid  (fig.  6).     The  level  of  the 
FIG.  6.  liquid  never  falls  sensibly  below 

the  neck  of  the  flask  if  the  latter 
is  notched.  If  the  liquid  can  be 
had,  like  water,  in  any  quantity,  a 
more  exactly  constant  level  is  got 
by  allowing  the  basin  to  continu- 
ally overflow  by  receiving  a  succession  of  drops  con- 


Bubble-size.  13 

taining  a  greater  supply  of  liquid  than  the  siphon  has 
to  deliver,  and  by  regulating  the  overflow  by  laying  a 
square  piece  of  linen  with  one  corner  hanging  over  the 
edge  of  the  basin.  This  acts  as  a  siphon  of  variable 
capacity.  In  the  case  of  mercury  the  linen  is  replaced 
by  a  piece  of  amalgamed  platinum  foil. 

§  1 4.  Bubbles, — The  cohesion  of  liquids  also  de- 
termines the  shapes  and  sizes  of  bubbles  properly  so 
called  ;  that  is,  masses  of  gas  liberated  in  the  midst  of 
a  liquid  and  finally  separated  from  their  sources  by 
the  buoyancy  of  the  surrounding  liquid.  Films  en- 
closing air  or  gas  are  also  called  bubbles.  The  bubble- 
size  of  a  gas  issuing  through  an  orifice  in  the  middle  of 
a  liquid  is  influenced  (i)  by  the  rate  at  which  the 
bubbles  succeed  one  another  (this  is  of  very  small 
effect) ;  (2)  nature  of  the  solid  from  which  the  gas  is 
delivered ;  (3)  size  of  orifice  and  distribution  of  solid 
about  it;  (4)  temperature  of  gas  and  liquid;  (5)  ten- 
sion of  gas  ;  (6)  nature  of  liquid. 

§  1 5.  The  apparatus  employed  is  shown  in  fig.  7. 
The  quart  bottle  A  is  filled  a  little  above  the  mark  a 
with  water,  which  in  some  experiments  is  covered  with 
a  film  of  oil.  Through  its  cork  three  tubes,  c  E  F,  pass 
absolutely  air-tight.  The  tube  c  is  a  simple  funnel 
tube  open  near  to  the  bottom  of  A.  The  tube  D  also 
reaches  to  the  bottom  of  A  and  acts  as  a  siphon.  Its 
longer  limb  is  narrowed  at  the  end,  and  delivers  its 
water  into  the  little  flask  M  whose  neck  bears  a  mark. 
The  shorter  limb  of  D  bears  a  cock  E  to  regulate 
its  discharge.  The  third  tube  F,  which  opens  imme- 
diately under  the  cork  of  A,  is  fastened  by  a  caout- 
chouc joint  to  the  tube  B.  In  this  joint,  and  pressing 


14  Practical  Physics. 

the  ends  of  both  tubes,  is  a  compact  mass  of  cotton 
wool.  B  passes  through  the  cork  of  the  little  test-tube 
G,  which  is  divided  into  millimeters  and  contains  the 
liquid  through  which  the  bubbles  are  to  pass. 

Through  the  cork  of  G  another  tube  H  is  passed, 
which  is  bent  round  near  the  lower  end  h  so  as  to  open 
upwards,  and  is  beneath  the  surface  of  the  liquid  in  G. 

FIG.  7. 


H  is  connected  by  a  caoutchouc  joint  with  i,  which 
passes  nearly  to  the  bottom  of  a  second  little  test-tube 
j.  The  tube  j  contains  a  few  drops  of  the  liquid  which 
is  in  G,  and  the  space  between  I  and  the  sides  of  j  is 
filled  with  cotton  wool  moistened  with  the  same  liquid. 
The  last  tube  K,  which  opens  immediately  under  the 
cork  of  j,  is  either  open  to  the  air  or  connected  with  a 
gas  bag  containing  the  gas  under  examination,  or 


Bubble-size.  1 5 

fastened  to  a  chloride  of  calcium  tube  according  to 
the  requirements  of  the  experiment.  In  some  experi- 
ments the  little  tubes  G  and  j  are  surrounded  with 
water  contained  in  the  vessel  N.  A  thermometer  T  is 
placed  in  the  water  of  N. 

The  apparatus  is  used  as  follows.  B  and  F  being 
disconnected,  the  bottle  A  is  nearly  filled  through  c. 
The  end  of  F  is  closed  by  the  finger,  and,  the  stop- 
cock E  being  opened,  the  siphon  D  is  filled  once  for 
all  by  applying  the  mouth  to  its  longer  end.  E  being 
then  closed,  the  tube  G  is  filled  up  to  the  required 
mark  with  the  liquid  which  is  to  serve  as  a  bubble 
medium.  The  cotton  wool  in  j  is  moistened  with  the 
same  liquid.  All  the  joints  are  made  fast,  and  the 
tube  K  is  connected  with  the  gas  bag  L.  On  turning 
the  stop-cock  E,  water  flows  through  the  siphon  D  into 
the  flask  M.  To  supply  its  place,  gas  must  enter  by 

F,  that  is,  gas  must  bubble  through  the  liquid  in  G. 
Before  entering  G  it  becomes  saturated  with  the  vapour 
of  the  same  liquid  in  j.     If  all  the  joints  are  tight,  it 
follows  that  the  volume  of  water  entering  M  is  equal  to 
the  volume  of  gas  which  bubbles  through  the  liquid  in 

G.  It  is  a  sufficient  test  of  the  tightness  of  all  the  joints 
(as  far  as  H)  to  run  off  a  little  water  by  D  so  as  to  bring 
a  bubble  or  two  of  the  gas  through  h  and  to  allow  the 
apparatus  to  rest.     If  the  tube  H  remains  full  of  air  to 
its  extremity  for  a  quarter  of  an  hour,  the  apparatus 
may  be  considered  as  air-tight.     A  metronome  is  ad- 
justed to  beat  to  the  required  time.    M  is  removed  and 
emptied.     E  is  turned  till  the  bubbles  passing  through 
the  liquid  in  G  keep  time  with  the  beats  of  the  metro- 
nome.  This  rate  is  maintained  till  the  liquid  in  A  sinks 


1 6  Practical  Physio*. 

to  a.  The  flask  M  is  then  put  in  its  place,  and  from 
that  instant  the  bubbles  passing  through  G  are  counted. 
When  M  is  filled  exactly  up  to  the  mark  the  experiment 
is  finished.  The  proximity  between  M  and  G  enables  the 
eye  to  count  the  bubbles  and  to  watch  without  diffi- 
culty, at  the  same  time,  the  rise  of  the  liquid  in  M.  The 
contents  of  M,  divided  by  the  number  of  bubbles,  gives 
the  mean  volume  of  a  single  bubble.  The  use  of  the 
cotton  wool  in  the  joint  between  B  and  F  is  to  check 
the  flow  of  gas  through  the  apparatus.  When  this 
plug  is  absent,  the  considerable  volume  of  gas  in  the 
upper  part  of  A,  being  in  direct  communication  with 
G,  causes  by  its  elasticity  an  irregular  delivery  of 
bubbles  through  G.  Of  course  as  M  is  filled,  the  level 
of  the  liquid  in  A  falls.  The  difference  between  the 
limbs  of  the  siphon  D  is  diminished  ;  the  flow  through 
D  is  retarded,  and  the  bubbles  follow  one  another 
more  slowly  ;  this,  however,  makes  exceedingly  little 
or  no  difference  in  the  size  of  the  bubbles. 

§  1 6.  The  radii  of  the  tubes  being  shown  in  column 
(i),  the  volumes  of  the  air  bubbles  delivered  from  the 
tubes  at  the  rate  of  i  bubble  in  2"  are  shown  in 
column  (2).  The  liquid  medium  is  water. 

(i)  (*) 

0-1428  0-035 

0*4595  0<I49 

0-6035  0-152 

1-4099  0-178 

17607  0-244 

2*0998  o'3I9 

§  17.  The   combined  effect  of  the  cohesion  and 


Bubble-size.  *%j 

specific  gravity  of  the  liquid  in  determining  the  bubble- 
size,  is  measured  by  altering  the  liquid  while  other 
circumstances  .are  maintained  the  same.  In  the  fol- 
lowing table  are  given  in  cubic  centimetres  the  bubble- 
sizes  of  air  passing  through  various  liquids. 

Mercury        .         .         .         .         .0-4120 

Glycerine 0-1145 

Water 0-0860 

Butyric  acid 0-0582 

Acetic  acid 0*0572 

Alcohol 0*0480 

Benzol  ......  0*0480 

Oil  of  Turpentine  ....  0*0453 

Acetic  ether  .....  0*0372 

In  determinations  of  this  last  kind  the  gas  bag  L  is 
replaced  by  a  chloride  of  calcium  tube.  The  cotton 
wool  of  j  is  saturated  with  the  liquid  under  examina- 
tion in  G,  so  that  the  bubbling  gas  is  dry  air  already 
saturated  with  the  vapour  of  the  liquid  through  which 
it  has  subsequently  to  bubble.  It  is  clear  that  if  the 
air  so  charged  were  to  come  into  contact  with  the 
water  in  A,  the  vapour  would  dissolve  in  the  water, 
while  the  air  would  become  moist.  A  difference  in 
volume  would  be  thereby  occasioned,  according  to  the 
difference  of  the  tension  of  the  vapour  of  the  liquid  in 
G  and  j  on  the  one  hand,  and  that  of  water  on  the 
other.  To  avoid  this  source  of  error,  the  vessel  A  is 
filled  with  mercury ;  and  after  each  experiment  the 
vessel  A  is  completely  refilled  with  mercury,  so  as  to 
expel  the  vapour  of  the  liquid  used  in  the  previous 
experiment.  The  mercury  is  then  run.  off  at  D  until 
c 


i8  Practical  Physics. 

it  falls  in  A,  nearly  to  the  mark  a.  The  liquid  under 
examination  in  G  should  have  a  height  above  h  in- 
versely as  its  specific  gravity.  This  is  easily  effected 
by  means  of  the  graduation  of  the  tube  G.  By  this 
means  the  pressure  on  the  gas  as  it  issues  from  h  is 
the  same  in  all  the  experiments.  The  vessels  A,  G, 
and  j  are  all  sunk  in  the  same  trough  of  water,  so 
'hat  the  volume  of  the  air  undergoes  no  alteration 
from  temperature,  either  during  or  after  its  passage 
through  G.  When  the  growth- time  of  the  bubbles  has 
"been  brought  exactly  to  the  pre-determined  value 
(say  2"),  and  the  mercury  in  A  has  sunk  to  a,  a 
graduated  burette  is  brought  under  the  siphon  D,  and 
kept  there  while  100  bubbles  pass  through  G. 

§  1 8.  The  size  of  an  air  bubble  iormed  under 
given  conditions  in  a  mixture  of  two  liquids,  A  and  B, 
is  a  mean  between  its  size  through  A  and  through  B. 
And  a  very  accurate  estimate  of  the  relative  quantities 
of  the  two  constituents  of  a  mixture  can  be  got  if  we 
know  the  bubble  size  in  each  constituent. 

§19.  Cohesion  of  Gases  Viscosity. — Although  a 
gaseous  mass  will  preserve  neither  its  shape  nor  its 
volume  unless  enclosed  by  Folid  or  liquid  walls,  and  is, 
'herefore,  destitute  of  that  cohesion  which  is  repre- 
sented by  hardness  and  form-elasticity,  it  offers,  accord- 
ing to  its  nature,  a  variable  resistance  to  bodies  passing 
through  it.  Now,  as  such  resistance  in  the  case  of 
solids  and  liquids  is  obviously  and  directly  associated 
with  their  hardness,  we  may  here  mention  the  chief 
direct  experiments  on  the  viscosity  of  gases.  This 
has  been  most  accurately  determined  in  a  direct  man- 
ner by  pendulum  experiments.  A  pendulum  is  made 


Volume-elasticity.  19 

to  swing,  beginning  with  a  given  arc,  in  a  chamber 
which  can  be  filled  with  any  gas.  By  raising  or 
lowering  a  mercury  valve,  a  constant  tension  of  the 
gas  in  the  chamber  can  be  obtained.  The  time 
occupied  by  the  pendulum  in  performing  a  given 
number  of  oscillations  is  noted.  A  more  exact  method 
is  to  place  timed  chronometers  under  bell-jars  con- 
taining various  gases,  and  also  in  vacuo. 


VOLUME-ELASTICITY  OF  SOLIDS,   LIQUIDS, 
AND  GASES. 

§  20.  No  direct  and  exact  measurements  have 
been  made  of  the  compressibility  of  solids.  For  sen- 
sible compression  such  enormous  pressures  are  re- 
quired, that  at  present  exact  measurements  are  wanting. 
And  even  with  most  liquids  the  compressibility  is  so 
small,  even  by  great  pressures,  that  special  '  piezome- 
ters '  are  used.  One  form  of  piezometer,  which  can  be 
made  without  much  difficulty,  is  shown 
in  fig.  8.  A  very  stout  glass  tube,  T, 
is  closed  at  the  bottom,  and  about 
half-way  up  in  its  side  two  platinum 
wires,  pl  p2,  are  fused  through  the  glass. 
Some  mercury  is  poured  in,  and  then 
two  tubes,  one  containing  air  and  the 
other  the  liquid  under  examination, 
both  being  closed  at  the  top  and  open  below,  are 
introduced,  so  as  to  stand  in  the  mercury.  Finally,  a 
little  dilute  sulphuric  acid  is  introduced,  so  as  to  cover 
c  2 


2O  Practical  Physics. 

the  platinum  wires,  and  the  tube  is  then  hermetically 
sealed.  On  connecting  p±  and  /2  with  the  poles  of 
a  two-cell  piatino-zinc  battery,  the  water  is  decom- 
posed into  its  two  elements,  which,  not  being  able  to 
escape,  exert  a  greater  and  greater  pressure  on  the 
sulphuric  acid,  and  thence  on  the  mercury  surface, 
and  so  compress  the  air  in  the  one  tube  and  the 
liquid  in  the  other.  As  we  shall  see  in  §  22,  the 
volume  of  a  given  mass  of  air  is  inversely  proportional 
to  the  pressure  upon  it.  Hence,  if  the  volume  of  air 
is  halved  by  the  pressure  thus  generated,  we  know 
that  the  pressure  is  doubled,  that  is,  instead  of  being 
exposed  to  one  atmosphere,  it  is  exposed  now  to  two, 
and  so  on.  It  is  not  safe  to  generate  a  pressure  of 
more  than  four  or  five  atmospheres  ;  and  it  is  dan- 
gerous to  allow  the  platinum  to  be  exposed  above  the 
liquid,  for  the  clean  platinum  may  determine  the  recom- 
bination of  the  elements  of  water  with  great  violence. 
§  21.  Elasticity  of  Gases  :  Relation  between 
Volume  and  Pressure. — It  appears  that  gases,  vapours, 
and  liquids  are  continuous  in  their  elastic  properties. 
The  gases  most  difficult  to  condense  are  hydrogen, 
nitrogen,  and  oxygen,  and  a  few  compound  gases.  The 
three  gases  named  follow  very  nearly  the  generalisation 
that  their  volume  varies  inversely  with  the  pressure 
to  which  they  are  subjected.  Substances  which  are 
gaseous  under  ordinary  conditions  of  temperature  and 
pressure,  may,  when  the  pressure  is  increased  or  the 
temperature  diminished,  become  liquids.  Such  hque- 
fiable  gases  are  often  called  vapours;  and  ihe  gene- 
ralisation which  connects  vapours  and  gases  is  that 
the  nearer  a  vapour  is  to  liquefaction,  either  by  in- 


Volume  and  Pressure  of  Gases.         21 


then 


thickly 
FIG.  9. 


and 


860 


creased  pressure  or  by  diminished  temperature,  the 
more  does  it  depart  from  the  generalisation  that  its 
volume  varies  inversely  as  the  pressure  upon  it. 

§  22.  A  tube  of  about  £  in.  internal  bore,  and  4  ft. 
long,  is  thoroughly  cleaned,  and  one  end  is  closed 
and  flattened  by  pressing  on  it  when  red  hot  a  piece 
of  flat  charcoal  ;  or  the  edge  may  be  turned  so  as  to 
form  a  lip,  and  a  well-fitting  cork  being  driven  in,  is 
tied  down  by  thin  copper  wire,  which  passes  also 
beneath  the  lip.  The  cork  is 
smoothly  covered  with  sealing- 
wax  (fig.  9).  The  tube  is  then 
bent  so  as  to  form  two  parallel 
limbs,  of  which  the  shorter, 
which  is  the  closed  end,  is  about 
6  in.  long.  It  is  now  fastened  to 
an  upright  support,  and  a  drop 
or  two  of  mercury  is  poured 
into  the  open  end,  so  as  just 
to  cover  the  bend  and  shut  off 
the  air  in  the  closed  limb. 
Adjust  a  millimeter  scale  to 
both  limbs  so  that  the  o  is  on  a 
level  with  the  mercury.  Sup- 
pose the  barometer  stands  at 
760  millimeters  of  mercury  at  the  time  of  the  expe- 
riment ;  and  suppose  that  the  top  of  the  closed  tube 
is  opposite  the  200  millimeter  mark  :  pour  mercury 
into  the  long  limb  until  the  mercury  in  the  short  limb 
stands  at  100;  the  mercury  in  the  longer  limb  will 
then  be  seen  to  stand  at  860,  that  is,  760  millimeters 
above  the  mercury  in  the  shorter  limb.  The  two 


22  Practical  Physics. 

columns,  each  100  mm.  long,  in  the  two  limbs  balance 
one  another.  Therefore,  in  order  to  halve  the  volume 
of  the  air  in  the  shorter  limb,  it  has  had  to  be  pressed 
by  an  additional  atmosphere.  A  similar  relationship 
is  observed  for  all  pressures.  On  compressing  a  gas, 
it  is  heated  ;  and  a  gas,  when  heated,  tries  to  expand. 
If,  therefore,  mercury  is  poured  suddenly  into  the 
longer  limb,  the  air  compressed  in  the  shorter  limb 
becomes  warm,  and  by  its  increased  tension  balances 
a  longer  column  than  it  would  when  cold.  Before 
finally  measuring,  the  apparatus  should  be  allowed  to 
stand  for  a  few  minutes  to  cool— say  thirty  minutes. 

§  23.  When  the  observations  of  gas-volumes  extend 
over  several  hours  during  which  the  barometric  pres- 
sure may  have  altered  and  has  perhaps  never  been 
the  mean  (760  mm.),  it  is  convenient  to  reduce  all 
observed  volumes  to  this  mean  pressure  in  order  to 
compare  them  fairly  with  one  another.  Thus  the  ob- 
served volume  of  a  gas  to-day  when  the  barometer 
is  754*2  mm.  is  69*22  c.c.  The  gas  would  measure 
at  760  mm. 

7*?  4"  2 
69*22  c.c.  x  -^-that  is,  68*69  c.c. 

In  general  terms  if  HJ,  H2  be  the  two  barometric 
heights,  and  z/,,  vz  be  the  corresponding  volumes 
of  the  same  mass  of  gas 

HI 

"»  =  Z''il 

Every  mass  of  matter  at  rest  is  of  course  exercising 
as  much  pressure  as  it  supports.  The  compressed 
gas  is  accordingly  exercising  a  pressure,  tension  or 
elasticity,  equal  to  the  compressing  force.  There 


Capillarity. 


23 


being  the  same  mass  (weight)  of  air  before  and  after 
the  compression,  doubling  the  pressure,  in  halving  the 
volume,  of  course  doubles  the  density. 


COHESION  OF  LIQUIDS  AFFECTED  BY  ADHESION 
TO  SOLIDS. 

§  24.  Capillarity. — It  is  found  experimentally  that 
the  height  to  which  a  liquid  rises  in  a  cylindrical  tube 
of  a  solid  which  it  wets,  is  inversely  proportional  to 
the  diameter  of  the  tube.  More  generally  expressed, 
when  a  tube  is  partly  plunged  into  a  liquid,  the  differ- 
ence in  height  between  the  inner  and  the  outer  liquid 
is  inversely  proportional  to  the  diameter  of  the  tube. 
That  this  is  approximately  true  is  seen  at  once  by 
binding  together  two  square  plates  of  glass  in  such  a 
way  that  they  form  an  angle  of  about  2°  opening. 
The  plates  are  wedged  slightly  apart 
along  one  edge  by  two  thin  bits  of 
cork,  and  the  opposite  edges  being 
brought  together,  a  vulcanised  caout- 
chouc band  is  passed  round.  On 
allowing  the  base  of  the  hollow 
prism  formed  by  the  plates  to  dip 
into  coloured  water,  the  latter  forms 
between  the  plates  an  open  curve, 
called  a  rectangular  hyperbola,  such  that  the  vertical 
height  of  any  point  of  the  curve  above  the  level  surface 
of  the  water  is  inversely  proportional  to  the  distance 
of  this  point  from  the  edge  along  which  the  plates 


FIG.  10. 


24  Practical  Physics. 

touch  each  other.  For  exact  measurements  and  veri- 
fication of  the  generalisation  above  given,  some  forn 
of  cathetometer  should  be  used  for  the  height  mea- 
surement, while  the  diameter  should  be  measured 
indirectly  by  ascertaining  the  length  of  a  certain 
length  of  a  known  liquid  filling  the  cavity  of  the 
capillary  tube. 

§  25.  Although  round  and  often  uniform  in  bore, 
the  ordinary  capillary  thermometer  tubes  are  unsuit- 
able for  such  experiments  on  account  of  the  great 
thickness  of  the  glass.  A  piece  of  glass  tube  is 
softened  and  drawn  out  to  about  6  ft.  as  uniformly 
as  possible.  The  central  part  of  this  is  taken  as 
being  the  most  uniform  in  bore.  A  little  mercury  is 
drawn  in,  and  the  thread  tube  being  laid  upon  a  scale, 
the  length  of  the  mercury  column  at  different  parts  ot 
the  tube  is  measured.  That  part  of  the  tube  where 
its  length  is  nearly  constant  may  be  employed.  Its 
diameter  is  determined  by  weighing  one  or  two  feet 
of  it  when  empty,  and  again  when  full  of  distilled 
water.  Let  its  weight  when  empty  be  14632  gram. 
Let  this  length  measure  563-2  millimeters,  and  sup- 
pose it  weighs  1-4740  when  full  of  distilled  water. 
The  cylinder  of  water  563-2  mm.  long  weighs  0-0108 
gram.  Then 

TT  r2  x  563-2  mm.  weighs  0*0108  gram. 
„  measures  0*0108  c.  c. 

„         io'S  c.  mm. 
r  =  0*0248  mm. 

If  the  tube  be  wide,  say  5  or  10  mm.  in  radius, 
mercury  may  with  advantage  be  substituted  for  water. 


FIG,  it. 


Capillarity.  2$ 

The  result  will  then  have  to  be  divided  by  the  specific 
gravity  of  mercury  (13*5).  But  with  narrow  tubes,  the 
film  of  air  between  the  mercury  and  the  glass  intro- 
duces a  sensible  error. 

The  diameters  of  two  tubes  having  been  thus 
determined,  they  may  be  laid  side  by  side  on  to  a 
freshly  varnished  paper  millimeter  scale  in  such  a 
way  that  their  ends  project  below.  The  scale  is  cut 
away  to  a  point  between  the  tubes  at  the  o  line.  The 
heights  are  then  at  once  read  off.  Very  exact  com- 
parative measurements  can  be  got  in  this  way  of  the 
capillary  heights  in  different  tubes  of  the  same  liquid. 
For  absolute  measurements  the  tubes  must  be  per- 
fectly vertical,  as  the  downward 
pressure  of  the  liquid  column  de- 
pends upon  the  height  of  the  top 
of  the  capillary  column  above  the 
level  in  the  reservoir,  and  not  upon 
the  absolute  length  of  the  column. 

§  26.  If  many  capillary  heights 
have  to  be  determined,  a  steel  mil- 
limeter scale  may  (fig.  n)  be  filed 
to  a  sharp  point  at  the  o  line,  tak- 
ing care  that  nothing  is  filed  off. 
Longitudinal  scratches  are  made 
along  the  scale  for  the  tubes  to 
rest  on,  and  they  are  fastened  to 
the  scale  by  a  little  soft  wax  or 
varnish.  The  scale  is  then  clamped 
vertically.  This  is  effected  by  comparing  one  of  its 
edges  with  two  plumb  lines  which,  as  seen  from  that 
edge,  appear  under  an  angle  of  about  90°.  The  vessel 


26  Practical  Physics. 

containing  the  liquid  is  then  placed  on  a  table  which 
can  be  raised  very  gradually  and  steadily  by  a  screw. 
After  the  scale  point  touches  the  liquid  the  latter  is 
further  raised  about  \  inch,  so  that  the  capillary  tubes 
may  be  wetted  inside  above  their  proper  level.  The 
liquid  is  then  lowered  and  the  point  of  the  scale 
wiped.  Finally  the  liquid  is  raised  very  slowly  and 
with  extreme  caution  till  the  point  touches  the  liquid. 
The  capillary  readings  may  be  at  once  taken  either 
by  the  naked  eye  or  with  a  pocket  lens,  or  through  a 
horizontal  telescope  moving  on  a  vertical  stand.  With 
narrow  tubes  the  latter  plan  has  no  sensible  advan- 
tage. 

§  27.  That  kind  of  capillarity  which  may  be  called 
negative  requires  in  general  for  its  measurement  a 
somewhat  different  form  of  apparatus.  Mercury  and 
glass  may  be  taken  to  represent  this  relationship. 
The  bore  of  the  capillary  tube  having  been  measured 
as  before,  it  is  connected  by  a  caoutchouc  tube 
(fig.  12)  with  a  wide  trans- 

FlG.    12.  ' 

parent  reservoir  of  mercury, 
such  as  a  wide  glass  tube 
drawn  out  at  the  bottom  and 
turned  up.  The  two  are  partly 
filled  with  mercury,  and  the 
levels  are  read  off  by  a  distant 
telescope  or  by  a  cathetometer. 
It  is  best  to  take  the  larger 

tube  so  wide  that  its  capillarity  can  be   neglected. 

The  depression  of  the  level   in  the  narrow  tube   is 

found  to  be  inversely  proportional  to  its  diameter  or 

radius. 


Capillarity. 


All  phenomena  of  capillarity  seem  to  show  that 
the  raising  or  lowering  of  the  liquid  level  is  brought 
about  by  the  shape  of  the  free  liquid  surface.  The 
shape  itself  is  determined  by  the  relation  between  the 
cohesion  of  the  liquid  and  the  adhesion  between  the 
liquid  and  solid. 

§  28.  If  we  immerse  fig.  13,  a  capillary  U~s^aPed 
tube,  in  water  so  that  its  shorter  limb  a  is  covered,  the 
liquid  stands  at  b  in  the  longer  limb  B.  On  with- 
drawing the  reservoir,  the  liquid  FIG.  13. 
surface  at  a  becomes  convex,  and 
there  is  a  certain  difference  in 
height  between  a'  and  b '.  On 
touching  the  convex  surface  at  a' 
with  blotting  paper,  some  of  the 
water  is  removed  and  the  surface  becomes  flatter. 
When  it  is  quite  flat  there  is  the  same  difference  if 
level  between  a'  and  b'  as  there  was  between  b  and 
the  liquid  in  the  reservoir.  Again  (fig.  14),  let  a  wide 

FIG.    14. 


tube  A  be  connected  with  a  capillary  tube  B.  Pour 
water  into  the  two,  and  you  get  a  definite  capillary 
elevation,  which  difference  is  maintained  until  the 
liquid  reaches  the  top  of  the  narrow  tube;  the  surface 
of  the  liquid  in  this  tube  then  begins  to  flatten,  and 
when  it  is  quite  flat  the  level  in  both  tubes  is  the 


28  Practical  Physics. 

same ;  on  adding  more  water  to  the  wider  tube,  the 
level  in  it  may  be  raised  considerably  above  that  in 
the  narrow  tube,  the  surface  in  which  becomes  then 
convex. 

§  29.  The  connection  between  the  curvature  and 
the  cohesion  and  adhesion  is  generally  attributed  to  an 
alteration  in  the  density  of  the  liquid  at  and  near  the 
solid.  Without  discussing  this  question,  the  relative 
capillarities  of  different  liquids  in  regard  to  the  same 
solid  can  be  at  once  measured  by  replacing  the  water 
of  §  26  by  other  liquids.  With  regard  to  the  variation 
effected  in  capillary  height  by  variation  in  the  solid, 
it  is  difficult,  if  not  impossible,  to  obtain  tubes  of 
exactly  the  same  diameter  and  of  different  material. 
And  although,  assuming  that  the  law  of  capillarity 
holds  good  with  all  solids  and  all  liquids,  we  might 
make  use  of  tubes  of  different  diameters,  it  is  far 
easier  to  apply  drop-size,  §§  12,  13,  for  this  purpose, 
for,  like  height,  drop-size  is  affected  positively  by  the 
increased  cohesion  of  the  liquid  and  negatively  by  its 
density.  In  most  cases  it  has  to  be  borne  in  mind 
that  the  surfaces  of  solid  bodies  are  coated  with  films 
of  air,  and  it  is  the  relationship  of  this  film  towards 
the  liquid  which  mainly,  at  all  events  at  the  first 
moment,  determines  the  capillarity.  In  the  vacuum 
of  the  most  perfect  barometers  the  surface  of  the 
mercury  is  perfectly  level,  and  allowance  for  capil- 
larity in  the  tube  rather  introduces  than  eliminates 
error. 


COHESION  OF  SOLIDS  AFFECTED  BY  THEIR 
ADHESION  TO  LIQUIDS.     SOLUTION. 

§  30.  The  degree  of  solubility  of  solids  in  liquids 
is  so  much  affected  by  temperature  that  it  will  have 
to  be  mainly  considered  in  connection  with  HEAT. 
Also  the  rate  of  solution  in  so  far  as  it  is  affected  by 
convection  currents  of  course  depends  upon  tempe- 
rature. With  regard  to  the  comparative  solubility  of 
salts  at  the  same  temperature,  a  few  hints  may  be 
here  given.  As  solutions  of  sdt  in  water  are  always 
heavier  than  water,  the  salt  in  order  to  saturate  the 
water  must  be  frequently  stirred  with  it,  or  far  better, 
it  is  hung  in  a  muslin  bag  at  the  surface  of  the  water. 
If,  as  is  almost  invariably  the  case,  it  is  more  soluble 
in  hot  than  in  cold  water,  it  is  heated  with  water  till 
the  water  is  so  far  saturated  FIG.  15. 

that  a  portion  ot  the  salt 
separates  out  on  cooling  to 
the  required  temperature.  If 
the  first  plan  is  adopted,  the 
solution  should  be  allowed 
to  evaporate  till  salt  begins 
to  separate. 

§  31.  To  determine  the 
quantity  of  salt  in  a  solu- 
tion, a  long-necked  flask 
of  hard  glass  is  dried  and 
weighed,  and  a  few  grams 
of  the  solution  being  introduced  by  a  pipette  without 
soiling  the  neck,  the  flask  and  solution  are  weighed 


3O  Practical  Physics. 

together.  The  flask  is  tilted  on  one  side,  and  the 
water  is  evaporated  off  without  boiling.  Such  evapo- 
ration may  be  advantageously  assisted  by  a  current  of 
air,  which  may  be  caused  to  flow  over  the  surface  of 
the  liquid  by  inserting  a  glass  tube,  /,  open  at  both 
ends,  and  heating  the  projecting  part,  which  there- 
upon acts  as  a  chimney.  Or  the  neck  of  the  flask 
may  be  connected  with  an  exhauster  such  as  a  water 
air-pump. 

§  32.  How  far  a  salt  may  be  heated  to  get  it 
anhydrous  without  decomposing  it  depends  upon  its 
chemical  nature,  and  for  this  and  for  the  determination 
of  the  quantity  of  the  salt  or  its  constituents  by  pre- 
cipitation, the  reader  is  referred  to  chemical  treatises. 
It  may  be  useful,  however,  to  know  for  physical 
experiments  that  the  following  amongst  the  more 
common  salts  become  perfectly  anhydrous  at  no0  C. 
without  undergoing  the  slightest  decomposition :  the 
chlorides,  bromides,  and  iodides  of  potassium  and 
sodium  ;  the  chloride  of  ammonium  ;  the  nitrates  of 
sodium,  potassium,  ammonium,  lead,  barium,  and 
silver ;  sulphate  of  potassium,  chromate  of  potassium, 
chlorate  of  potassium,  bichromate  of  potassium,  etc. 

§  33.  Diffusion  of  Liquids  into  Liquids. — The 
solution  of  a  salt  in  a  liquid  only  presents  the  simple 
condition  of  contact  between  pure  salt  and  pure  water 
at  the  first  instant  of  contact.  Immediately  after- 
wards the  salt  is  surrounded  by  a  salt  solution,  and 
this  again  by  water.  Further  mixture  is  then  brought 
about  by  the  passage  of  salt  from  the  salt  solution 
into  the  water>  for  it  is  this  passage  which  enables 
fresh  portions  of  the  salt  to  leave  the  mass.  The 


Diffusion  of  Liquids.  31 

mixture  of  a  salt  with  water  by  diffusion  appears  to  be 
due  to  the  motion  of  the  salt  itself,  and  not  to  the 
solution  of  it. 

§  34.  The  diffusion  of  salts  through  water  may  be 
measured  by  the  arrangement  represented  in  fig.  16. 

A  cylindrical  vessel  about   i  in.  diam. 

, J  •     ,  •  ,.      ,       ,  , 

and  4  in.  high  is  placed  on  a  glass  sup- 
port in  a  beaker;  the  cylinder  is  filled 
up  to  the  brim  with  a  solution  of  a  salt 
of  known  strength,  say  6  per  cent.  Water 
is  then  poured  into  the  beaker  so  as  to 
be  about  J  in.  above  the  edge  of  the 
cylinder.  Diffusion  at  once  begins,  the 
salt  solution  pours  over  the  edge  of  the  cylinder,  and 
is  replaced  by  nearly  pure  water  at  the  mouth  of  the 
cylinder.  After  the  lapse  of  a  given  time,  the  con- 
tents of  the  beaker  are  run  off  by  a  siphon  into  a 
basin,  into  which  the  outside  of  the  cylinder,  the 
stand  and  the  beaker  are  all  washed.  The  amount  of 
dry  salt  is  determined  by  evaporation  and, weighing 
the  residue,  as  in  §  31.  A  6  per  cent,  solution  of 
some  other  salt  being  experimented  on  under  like 
conditions,  the  ratio  between  the  two  residues  is  the 
relative  diffusion.  It  is  obvious  that  this  kind  of 
experiment  is  so  far  defective  as  after  a  time  the 
diffusion  of  the  salt  takes  place  into  a  salt  solution 
instead  of  into  water.  And  this  occurs  soonest  with 
those  solutions  whose  diffusion  is  the  greatest. 

§  35.  Chloride  of  potassium  and  sulphate  of  potas- 
sium are  convenient  salts  to  compare,  for  they  differ 
considerably  in  diffusibility  (in  the  ratio  of  i  to  0*6987) 
and  are  both  readily  estimated  by  evaporation.  On 


32  Practical  Physics. 

comparing  in  this  way  solutions  of  various  strengths 
of  the  same  salts,  the  generalisation  is  established 
that  the  rate  at  which  a  soluble  salt  diffuses  from  a 
stronger  to  a  weaker  solution  is  approximately  pro- 
portional to  the  difference  of  strength  between  two 
contiguous  strata. 

§  36.  Diffusion  of  Gases  into  Liquids.    Absorp- 
tion.— A  simple,  and  for  most  purposes  sufficiently 

FIG.  17. 


d)  (2)  (3)  (4) 

exact  absorptiometer,  is  constructed  and  used  as  fol- 
lows. A  tube  (fig.  17)  a,  about  the  diameter  of  a 
burette,  is  drawn  to  a  neck  in  the  middle,  and  a  very 
well-fitting  glass  stop-cock,  £,  is  then  inserted.  Both 
above  and  below  the  cock  a  millimeter  scale  is 
etched  on  the  glass,  and  the  tube  is  calibrated.  By 
a  cork  fitting  the  top,  and  a  piece  of  tubing  through 
the  cork,  mercury  is  drawn  up  out  of  a  trough  past 


Absorption  of  Gases  by  Liquids.         33 

the  stop-cock,  which  is  then  turned  off.  The  gas  to 
be  examined  is  introduced  below,  and  the  liquid  (say 
thoroughly  boiled  water)  is  put  into  the  upper  tube. 
The  cock  is  now  turned  till  the  whole  of  the  mercury, 
but  none  of  the  water,  has  passed  into  the  lower  tube. 
It  is  then  turned  off,  and  the  level  of  the  liquid  read 
off  in  the  upper  tube,  and  that  of  the  mercury  in  the 
lower  one  (2).  Next  the  cock  is  turned,  and  some 
of  the  water  is  run  in.  The  quantity  is  known  from 
the  sinking  of  the  water  in  the  upper  tube,  and  the 
applied  calibration  of  that  part.  After  standing  a  few 
minutes,  the  thumb  well  smeared  with  burnt  caout- 
chouc is  pressed  upon  the  opening  of  the  lower  tube, 
and  the  whole  is  taken  out  of  the  mercury  trough  and 
well  shaken.  This  is  done  several  times  at  intervals, 
the  tube  always  being  opened  under  the  mercury. 
Finally,  the  whole,  mercury  trough  and  all,  is  placed 
in  a  capacious  beaker,  and  surrounded  with  water  of 
the  temperature  of  the  air,  and  the  height  of  the  mer- 
cury read  off  (3).  The  pressure  to  which  the  gas  is 
subjected,  and  under  which  absorption  has  taken 
place,  is  measured  by  the  barometric  pressure  at  the 
time  diminished  by  the  difference  between  the  heights 
of  the  mercury  inside  and  outside  the  tube.  The 
inside  column  is  assisted  by  the  column  of  water 
above  the  mercury.  If  we  wish  to  experiment  with 
pressures  above  the  atmospheric,  a  bent  tube,  c  (4), 
the  shorter  limb  of  which  passes  through  a  caoutchouc 
stopper,  is  fixed  into  the  lower  end  of  the  absorption 
tube,  and  any  required  quantity  of  mercury  is  forced 
into  c  till  a  given  pressure  is  reached. 

§  37.  It  seems  that  the  quantity  (mass,  weight) 
D 


34  Practical  Physics. 

of  a  given  gas  which  a  given  liquid  absorbs,  is  almost 
exactly  directly  proportional  to  the  pressure.  Since 
the  density  varies  directly  as  the  pressure,  it  follows 
that  a  liquid  absorbs  the  same  constant  volume  of  a 
given  gas,  whatever  the  pressure  may  be.  The  *  co- 
efficient of  absorption '  is  the  volume  in  cubic  centi- 
meters (reduced  to  76  cm.  pressure  and  o°  C.)  of 
the  gas  which  i  cubic  centimeter  of  the  liquid  absorbs 
at  atmospheric  pressure  (76  cm.).  This  coefficient 
varies  greatly  with  the  temperature,  the  quantity  ab- 
sorbed being  always  less  at  higher  than  at  lower  tem- 
peratures. The  coefficient  of  absorption  should 
therefore  be  referred  to  some  fixed  temperature,  say 
o°C. 

§  38.  Condensation  of  Gases  by  Solids.  Occlusion. 
— Porosity  seems  to  be  always  comparative,  so  that 
condensation  of  gases  into  the  pores  of  solid  bodies 
is  continuous  with  the  penetration  of  a  gas  into  the 
densest  metals.  To  measure  exactly  the  volume  of  a 
gas  which  a  solid  will  absorb,  the  gas  may  generally 
be  collected  over  mercury  in  a  graduated  and  cali- 
brated tube.  The  solid  which  has  to  effect  the  absorp- 
tion must  be  first  deprived  of  any  gas  which  may  be  in 
it.  For  a  mere  qualitative  experiment,  that  is,  to  show 
the  fact  of  absorption,  the  solid  should  be  heated  as  hot 
as  it  will  bear  in  an  air-gas  flame,  and  be  plunged  under 
the  surface  of  mercury.  This  process  answers  well  with 
charcoal.  A  barometer  tube  is  filled  with  dry  gaseous 
ammonia,  so  that  the  mercury  is  at  the  same  height 
inside  as  outside  the  tube,  and  the  gas  is  therefore  at 
atmospheric  pressure.  Now  pass  up  a  pellet  of  hard 
charcoal,  which  has  been  heated  and  quenched  as 


Condensation.     Occlusion.  35 

described,  into  the  gas  :  absorption  at  once  begins, 
and  the  charcoal  absorbs  nearly  a  hundred  times  its 
own  volume.  To  measure  the  absorp-  FlG 
tion  exactly,  a  pellet  of  hard  charcoal, 
such  as  cocoanut  charcoal,  is  placed  in  a 
tube,  one  end  of  which  is  closed ;  the 
other  end  is  fastened  to  the  mercury  air- 
pump,  and  the  glass  is  heated  as  hot  as 
it  can  be  without  softening  while  the 
pump  is  in  action.  The  caoutchouc  joint 
connecting  with  the  pump  is  drawn  out 
and  pinched  off,  so  as  to  preserve  the  vacuum,  and 
the  glass  tube,  pellet  of  charcoal,  and  caoutchouc,  are 
weighed  together.  Then  the  caoutchouc  is  pulled 
off,  the  pellet  rolled  out  on  to  the  mercury,  imme- 
diately plunged  beneath  its  surface,  and  introduced 
into  the  gas.  It  is  better  even  to  heat  it  again  in 
forceps  as  high  as  possible  without  burning  it.  The 
tube  and  caoutchouc  are  again  weighed  by  themselves. 
After  absorption  appears  complete,  the  eudiometer 
should  be  removed  to  a  deep  mercury  well  and  lowered 
into  it,  till  there  is  the  same  level  inside  as  out.  The 
temperature  is  measured  by  enclosing  the  whole  in  a 
glass  cylinder  full  of  water  of  observable  temperature. 
Diminished  by  increased  temperature,  the  gas-absorb- 
ing power  of  a  solid  appears  to  depend  both  upon  the 
extent  of  the  porous  surface,  and  on  the  density  of 
the  solid.  It  also  appears  that  the  more  easily  a 
vapour  is  condensible,  the  greater  is  its  faculty  for 
being  absorbed.  While  some  metals  act,  like  silver, 
which  absorbs  oxygen  while  melted  and  gives  it  up  as 
it  cools,  most  metals  condense  gases  on  their  surfaces 
D  2 


36  Practical  Physics. 

and  absorb  them  into  themselves  to  the  greatest  degree 
when  they  are  cold. 

§  39.  If  chloride  of  ammonium  be  added  to  chlo- 
ride of  platinum,  an  almost  insoluble  double  chloride 
is  formed,  which,  after  slight  washing,  may  be  strongly 
heated.  Everything  excepting  metallic  platinum  is 
driven  off,  and  this  metal  then  presents  the  appearance 
of  a  spongy  grey  mass.  Held  on  a  platinum  wire,  a 
pellet  of  this  will  ignite  a  jet  of  hydrogen.  Brought 
into  oxygen  over  mercury,  it  condenses  and  absorbs 
that  gas. 

The  gases  which  have  been  absorbed  by  solids 
can  be  generally  detected  and  prepared  for  examina- 
tion by  heating  the  solid  in  a  hard  glass  tube  in  con- 
nection with  the  mercury  air-pump.  The  gases 
expelled  are  carried  down  the  moving  column  of 
mercury,  and  are  delivered  below. 

§  40.  It  is  probable  that  occlusion  is  similar  in 
kind  to  absorption,  but  as  it  takes  place  in  compact 
solids,  a  different  name  has  been  given  to  it.  Metal- 
lic iron,  when  heated  and  cooled  in  a  current  of  hydro- 
gen, absorbs  and  retains  about  2^5  times  its  volume  of 
hydrogen.  If  iron  be  deposited  electrolytically  in  a 
continuous  film,  which  is  done  by  electrolysing  a 
solution  of  the  ammonio-  sulphate  of  iron,  a  still  larger 
proportion  of  hydrogen  is  occluded.  When  hydro- 
gen is  evolved  electrolytically  at  the  surface  of  metal- 
lic palladium,  the  metal  absorbs  nearly  1,000  times 
its  own  volume  of  hydrogen  without  losing  its  lustre. 
The  volume  of  the  palladium  is  increased  during  the 
absorption,  and  this  causes  it  to  curl  and  twist  in  a 
remarkable  manner. 


Breath  Pictures.  37. 

§  41.  So  great  is  the  attraction  between  some 
solids  and  the  vapours  of  some  volatile  liquids,  that 
it  affords  the  means  of  producing  extremely  perfect 
vacua.  A  piece  of  cocoanut  charcoal  is  placed  in  a 
hard  glass  tube,  which  is  then  drawn  out  at  both 
ends,  and  contracted  to  narrow  necks.  To  one  end 
is  sealed  by  fusion  a  small  retort  containing  liquid 
bromine.  This  is  heated  till  it  boils,  while  the 
carbon  is  heated  as  hot  as  the  glass  will  bear.  The 
further  end  is  then  fused  off,  and  the  retort  is  also 
fused  off.  As  the  tube  cools  the  bromine  vapour 
disappears,  being  absorbed  by  the  carbon,  and  this 
absorption  is  so  complete,  that  if  two  platinum  wires 
have  been  previously  fused  into  the  tube  at  a  very 
small  interval  apart,  it  is  found,  as  long  as  the  char- 
coal is  cold,  that  the  interval  between  them  is  so 
perfect  a  non-conductor  for  electricity  that  no  dis- 
charge takes  place  between  them  when  they  are  con- 
nected with  the  terminals  of  an  induction  coil  of  such 
strength  that,  in  air  of  the  ordinary  tension,  a  spark 
of  several  inches  in  length  is  produced.  This  implies 
the  existence  of  as  perfect  a  vacuum  as  can  be  got  by 
the  most  perfect  arrangement  of  the  mercury  air- 
pump. 

§  42.  Breath  Pictures.— The  film  of  air  which 
covers  most  surfaces  has  a  different  power  of  con- 
densing vapours  from  that  possessed  by  the  bare 
surface  of  the  solid.  Hence,  if  we  rub  a  clean  sheet 
of  glass  with  a  point  of  hard  wood  or  brass,  the  air- 
film  is  rubbed  off  at  the  lines  of  contact,  and  on 
breathing  upon  the  glass  the  invisible  lines  become 
visible,  for  the  vapour  in  the  breath  is  not  condensed 


,38  Practical  Physics. 

upon  them.  Exposed  to  the  vapour  of  mercury,  the 
invisible  writing  on  a  glass  plate  may  be  made  per- 
manent. Such  breath  pictures  are  best  examined  by 
means  of  daguerreotype  plates,  that  is,  plates  of  copper 
covered  with  silver.  These  are  so  sensitive  that  they 
will  furnish  a  print  of  a  medal  or  other  body  which  is 
not  even  in  contact  with  them.  Such  a  plate  will 
condense  the  water  of  the  breath  as  a  brownish  dew 
where  there  is  a  film  of  air  or  gas,  but  as  a  bluish  dew 
where  there  is  none.  To  cover  the  plate  with  gas- 
film  it  is  covered  with  charcoal  which  has  been  satu- 
rated with  that  gas,  while  to  get  it  quite  free  it  is 
covered  with  charcoal  which  has  been  freshly  ignited, 
and  kept  covered  while  cooling.  Jf,  now,  the  plate 
has  been  saturated  wiih  a  gas,  say  carbonic  acid,  by 
the  first  plan,  and  a  medallion  is  placed  on  it  which 
has  been  deprived  of  all  gas  .by  the  second,  the 
medallion  surface  will  lay  hold  of  a  portion  of  the 
carbonic  acid  of  the  plate,  and  abstract  more  the 
nearer  it  is  to  the  plate.  On  afterwards  breathing  on 
the  plate,  the  parts  of  the  plate  which  were  nearest  to 
the  medallion  will  be  covered  with  a  bluish  dew,  the 
other  parts  with  a  brownish  dew.  This  shows  that 
the  metallic  surfaces  can  exert  actions  upon  each 
other  at  perceptible  distances  ;  possibly  every  metal- 
lic surface  is  in  a  similar  condition  to  that  of  a  free 
surface  of  mercury,  which  is  found  to  be  clothed  with 
an  atmosphere  of  mercury  vapour,  so  closely  bound 
to  the  liquid,  that  at  ordinary  temperatures  and  atmo- 
spheric pressures  its  presence  cannot  be  detected  at 
•i  millimeter  above  the  surface,  and  which,  in  still  air, 
protects  the  mercury  from  further  vaporisation. 


Diffusion  of  Gases.  39 

§  43.  Diffusion  of  Gases  into  Gases. — The  unham- 
pered diffusion  of  gases  into  gases  has  been  but  little 
studied.  The  essential  conditions  for  experiment  are 
of  course  that  the  heavier  gas  should  be  below,  that 
the  two  should,  at  a  given  time,  be  brought  into  con- 
tact without  disturbance,  and  that  the  condition  of  the 
mixture  at  the  end  of  a  given  time  should  be  ascer- 
tainable  without  disturbance. 

§  44.  That  gases  mix  with  one  another  rapidly 
and  perfectly  by  diffusion  is  seen  by  filling  two  wide- 
mouthed  bottles  over  water  with  any  two  gases,  cover- 
ing their  mouths  with  glass  plates,  turning  that  one 
over  which  contains  the  lighter  gas  and  placing  it  on 
t  e  other  one  so  that  the  two  plates  are  in  contact. 
On  sliding  the  plates  out  and  replacing  them  after 
only  a  few  seconds  the  contents  of  the  two  are  found 
to  be  identical :  namely  half  and  half,  if  the  vessels  are 
of  equal  capacity.  This  beinsj  so  it  follows  that  half 
the  number  of  atoms  of  the  lower  gas  have  passed  up 
and  half  those  of  the  upper  have  passed  down  through 
the  original  common  surface  at  the  vessels'  mouths. 
But  it  by  no  means  follows  from  this  that  the  diffusive 
energy  of  A  into  B  is  equal  to  the  diffusive  energy  of 
B  into  A,  because  under  the  condition,  the  sum  of  the 
volumes  being  constant,  the  diffusion  of  A  into  B  may 
be  both  a  cause  and  a  consequence  of  the  diffusion 
of  B  into  A. 

And  this  being  true  also  when  one  of  the  gases  is 
unlimited  in  volume,  makes  the  apparently  simple 
phenomenon  really  a  complex  one,  even  when  the 
vessel  has  the  simplest  (cylindrical)  form.  A  glass 
cylinder  A  (fig.  19),  about  6  in.  long  and  i  in.  internal 


1 


4O  Practical  Physics. 

diameter,  is  closed  at  one  end,  the  other  end  has 
ground  into  it  a  glass  stopper  carrying  a  tube  an  inch 
FIG.  19.  long  and  J  in.  internal  diameter  ground  flat 
on  the  top.  The  stopper  being  greased,  the 
cylinder  and  tube  are  filled  with  mercury  and 
then  by  displacement  nearly  filled  with  the 
gas.  A  glass  plate  is  pressed  on  to  the  end 
of  the  narrow  tube  and  the  whole  is  carried 
to  a  room  of  uniform  temperature  where  it  is 
supported  in  a  clamp.  If  the  gas  be  lighter 
than  air  (nitrogen,  hydrogen,  coal  gas)  the 
narrow  tube  is  directed  downwards — other- 
wise upwards.  The  glass  plate  is  removed  for  a  given 
interval  of  time.  It  is  then  replaced  and  the  mercury 
shaken  up  in  the  two  tubes.  A  sample  of  the  gas  is  then 
taken  out  for  analysis.  The  actual  quantity  of  the  gas 
which  has  diffused  out  is  proportional  with  the  same 
gas  to  the  sectional  area  of  the  exposed  surface.  The 
generalisation  which  has  been  established  experimen- 
tally is  that  with  different  gases  under  the  same  con- 
ditions the  quantities  vary  inversely  as  the  square 
roots  of  the  specific  gravities.  This  generalisation  is 
more  closely  reached  if  instead  of  one  large  surface 
FIG.  20.  of  contact  a  number  of  small 

ones  are  used,  such  as  exist 
in  a  thin  plate  of  plaster  of 
Paris,    or    artificial    graphite. 
And  the  adoption  of  such  a 
•^  device  enables  us  to  measure 
"^^  the  ratio  of  exchange  between 
two   gases    in   the    following 
manner.     A  glass  tube  A  (fig.  20)  is  fitted  with  a  solid 


Diffusion  of  Gases.  41 

cylindrical  plug  which  is  pushed  in  to  about  J  in.  from 
the  end.  Fine  plaster  of  Paris  paste  is  poured  upon 
the  top  of  the  plug.  After  a  time  the  latter  is  with- 
drawn and  the  plaster  is  allowed  to  dry  for  a  day  or 
two.  A  piece  of  sheet  caoutchouc  is  stretched  over  it 
and  tied  tightly  round  the  tqp.  The  tube  is  filled  with 
a  gas  over  mercury.  The  caoutchouc  is  taken  off,  and 
diffusion  through  the  plaster  at  once  begins.  In  the 
case  of  gases  lighter  than  air  the  mercury  is  seen  to 
rise  in  the  tube.  With  gases  heavier  than  air  it  falls. 
Since  difference  of  pressure  affects  the  rate,  it  is  ne- 
cessary to  keep  the  pressure  constant.  This  is  done 
either  by  dropping  mercury  into  the  trough  from  a 
pipette  or  letting  it  run  out  through  a  siphon.  By 
constant  watchfulness  the  mercury  is  kept  at  the  same 
level  inside  as  out.  After  a  time  the  caoutchouc  cover- 
ing is  tied  on  again  and  a  sample  of  the  gas  analysed. 
Or  another  way  of  performing  the  experiment  is  to 
maintain  the  level  as  long  as  any  tendency  to  change 
manifests  itself.  The  volume  of  the  air  (nearly  pure 
atmospheric)  which  is  now  in  the  tube  is  compared 
with  the  volume  of  gas  originally  in  the  tube,  and 
the  second  divided  by  the  first  is  the  specific  diffusion 
of  the  gas  in  regard  to  air.  As  however  air  itself  is  a 
mixture,  the  constituents  of  which  have  slightly  diffe- 
rent diffusion  rates,  the  gas  which  has  replaced  the 
escaped  gas  is  not  quite  pure  air:  it  is  rather  richer  in 
nitrogen.  The  absolute  error  introduced  on  this 
account  is  very  small,  and  the  error  affecting  the  com- 
parison between  two  gases  in  the  tube  is  only  a  small 
fraction  of  the  absolute  error.  The  whole  apparatus 
may  be  enclosed  in  a  bell-jar  of  continually  renewed 


42  Practical  Physics. 

carbonic  acid,  while  the  adjustment  of  the  level  of 
the  mercury  may  be  effected  by  tubes  passing  through 
the  supporting  table. 

§  45.  The  same  relation  is  found  to  exist  (when 
the  porous  plate  is  thin)  between  the  diffusive  powers 
through  plates  as  that  which  exists  with  free  intercourse, 
namely  that  the  volume  passing  varies  inversely  with 
the  square  root  of  the  specific  gravity  of  the  gas.  So 
that  if  the  tube  A  were  filled  with  hydrogen  (density  =  i) 
and  surrounded  by  oxygen  (density =i  6),  four  vols.  of 
hydrogen  (\/i6)  would  pass  out  for  every  i  vol.  of 
oxygen  (N/I)  which  entered.  When  all  the  hydrogen 
had  escaped  therefore  the  distance  between  the  mer- 
cury and  the  plaster  would  be  one-fourth  of  what  it 
was  when  the  tube  was  full  of  hydrogen,  supposing 
the  pressure  to  have  remained  the  same  throughout 
on  both  sides  of  the  plaster. 

§  46.  To  merely  exhibit  this  differential  diffusion,  two 
round  porous  earthenware  battery  cells  a,  b,  are  fastened 
FIG.  ax.  by  caoutchouc  connectors  to 

a  glass  tube  c  from  which  a 
G  horizontal  tube  d  bent  at  right 
angles  enters  a  safety  flask  e, 
through  whose  cork  passes  a 
second  tube /"which  dips  into 
coloured  water  ;  on  placing  a 
bell-jar  G  containing  hydrogen 
or  coal  gas  over  a,  air  is  driven 
out  of/;  on  filling  the  jar  G  with  carbonic  acid  and 
surrounding  b  with  it,  the  liquid  in/ rises. 

§  47.  Effusion. — A  distinction  is  generally  made 
between  the  passage  of  one  gas  into  another  by 


Effusion  of  Gases.  43 

diffusion  through  porous  solid,  which  is  always  a  reci- 
procal motion,  and  the  passage  of  a  gas  through  one 
or  more  holes  in  a  solid  into  a  more  or  less  complete 
vacuum.  The  first  kind  of  motion  is  in  the  strictest 
sense  molecular,  for  on  mixing  gases  the  molecules  of 
each  are  separate.  The  gas  in  the  second  case  moves 
in  currents. 

§  48.  A  hole  not  larger  than  a  pin-hole  is  bored 
through  a  thin  circular  plate  of  brass  or  platinum. 
The  sides  of  the  hole  are  hammered  and  the  hole  re- 
bored  until  under  a  hand  lens  the  edges  appear  flat 
and  smooth  (fig.  22)  The  edge  of  the  plate  is  then 
coated  with  a  rim  of  shel- 

-  IT  I  •  FlG-    22' 

lac  and  dropped  into  a 
glass  tube  having  a  waist 
narrower  than  the  metal 

disc.  The  whole  is  held  nearly  vertically  and  warmed 
to  melt  the  shellac,  so  that  a  perfectly  air-tight  con- 
nection is  made.  One  end  of  the  tube  is  drawn  out 
and  bent  down  so  as  to  serve  as  a  delivery  tube ;  the 
other  is  connected  with  an  apparatus  to  be  described 
m  §  59,  whereby  a  constant  pressure  is  maintained. 
The  quantity  of  gas  which  passes  through  the  per- 
foration in  a  given  time  is  measured.  The  motion  is 
here  caused  of  course  by  the  difference  of  pressure  on 
the  two  sides  of  the  hole,  the  pressure  at  one  side 
being  that  of  the  atmosphere.  To  measure  what  is 
generally  understood  by  effusion  the  end  a  is  left  open 
and  the  end  b  is  connected  with  a  mercury  air-pump. 
The  gas  which  is  drawn  out  of  b  is  collected  and 
measured.  For  gases  other  than  air  the  gas  is  placed 
in  a  loose  bag  connected  with  a.  A  convenient  form 


44 


Practical  Physics. 


of  orifice  for  effusion  experiments  is  shown  in  fig.  23, 
where  the  glass  tube  a  is  heated 
at  its  end  and  allowed  nearly 


FJG 


another  tube  with  shellac.  For  openings  which  are  so 
large  that  the  mercury  air-pump  cannot  be  depended 
on  for  maintaining  a  constant  vacuum,  an  ordinary 
air-pump  with  a  barometer  gauge  will  answer,  but 
there  should  be  interposed  between  the  pump  and 
the  tube  a  reservoir  vacuum.  The  gas  may  in  this 
case  be  contained  in  a  gasometer,  which  must  be 
maintained  so  as  to  give  a  constant  pressure. 

§  49.  Diffusion  of  Liquids  into  Gases.  —  In  §§  44- 
46  it  appeared  that  when  one  gas  diffused  into  an- 
other, the  second  diffused  into  the  first.  It  appears 
also  that  whenever  a  gas  is  soluble  in  a  liquid  the 
liquid  is  aerifiable  into  the  gas.  The  cohesion  of 
liquids,  whereby  their  aerification  is  restrained,  de- 
pends so  much  upon  their  temperature  that  we  shall 
have  to  reconsider  the  question  under  HEAT.  The 

apparatus  used  for  mea- 
suring the  rate  of  eva- 
poration which  liquids 
exhibit  under  like  con- 
ditions is  as  follows. 
The  gas  which  is  to 
effect  the  evaporation 
enters  at  a  from  a  limp 
bag  ;  and  it  is  drawn 
over  the  liquid  by 
means  of  the  flow  of 
The  liquid  to  be 


FIG.  24. 


et 

water  from  the  gas-holder,  G. 


Evaporation.     Vapottr  Tension.          45 

evaporated  is  in  the  cylindrical  vessel.  At  the  bottom 
of  v  is  a  considerable  quantity  of  mercury,  above  which 
is  the  liquid.  The  tube  for  the  entrance  of  the  gas  is 
widened  into  a  funnel-shape,  and  the  throat  of  the 
funnel  is  partly  choked  with  cotton-wool.  The  cork  is 
made  tight  with  a  large  quantity  of  shellac,  having  a 
smooth  surface.  The  gas  exit  and  entrance  tubes  pass 
water-tight  through  the  sides  of  a  vessel  containing 
water.  The  water  maintains  the  temperature  constant. 
The  mercury  prevents  v  from  floating.  The  funnel- 
shaped  opening  containing  cotton-wool  prevents  the 
liquid  from  presenting  an  irregular  surface  through 
disturbance.  Dry  air  is  first  passed  through  the  ap- 
paratus, so  as  to  dry  up  any  of  the  liquid  which  is 
sticking  to  the  glass.  The  whole  is  wiped  dry  and 
weighed.  Having  been  put  together  and  the  joints 
made  tight,  a  known  quantity  of  water  is  allowed  to 
flow  out  of  G.  and  that  this  flow  should  be  uniform  it 
should  be  delivered  into  litre  flasks  of  which  one  may 
fill  every  five  minutes.  After  a  known  quantity  of  air 
or  gas  has  been  drawn  over,  the  vessel  v  is  removed, 
dried,  and  re-weighed. 

§  50.  Experiments  show  that  the  more  a  gas  is 
soluble  in  a  liquid  the  more  is  the  liquid  volatile  in 
the  gas.  Thus  water  is  more  volatile  in  oxygen  than 
in  hydrogen,  or  nitrogen,  or  olefiant  gas,  while  alcohol 
is  more  volatile  in  the  latter  gas  than  in  any  of  the 
others.  Water  at  its  maximum  density,  that  is  4°  C., 
is  less  volatile  than  at  higher  or  lower  temperatures. 
Such  differences  only  refer  to  the  rate  and  not  to  the 
final  amount  of  the  liquid  volatilised.  For  if  a  liquid 
be  introduced  into  a  gas  in  a  barometer  tube  standing 


46  Practical  Physics. 

over  mercury,  the  depression  of  the  mercury  will  be 
the  same  whatever  be  the  nature  of  the  gas,  showing 
that  the  same  quantity  or  volume  of  vapour  has  been 
formed. 

§  51.  Vapour  Tension. — Looking  upon  a  liquid 
evaporating  in  the  air,  we  find  the  evaporation  pro- 
ceed against  and  overcome  the  air  pressure.  In 
order  to  find  with  what  pressure  the  vapour  separates 
itself  from  the  parent  liquid,  that  is  the  vapour  tension 
of  the  liquid,  the  atmospheric  pressure  must  be  re- 
moved. It  is  clear  that  a  body  in  the  barometric 
vacuum  is  not  subject  to  any  pressure  at  all,  and 
accordingly  if  a  liquid  be  introduced  into  the  vacuum 
the  depression  it  causes  in  the  mercury  measures  its 
spring  or  vapour  tension. 

§52.  For  most  purposes  the  simple  *  eudiometer' 
tube  serves  for  such  measurement.  A  millimeter 
scale  is  either  etched  on  the  tube  or  supported 
closely  behind  it,  the  readings  being  taken  through  a 
vertically  sliding  telescope.  In  comparing  different 
liquids  at  the  same  temperature,  if  that  tempera- 
ture be  the  atmospheric,  the  barometer  tube  after 
being  filled  with  mercury  is  inverted  into  a  trough 
having  plate-glass  sides.  The  height  is  measured 
inside  and  outside  the  tube,  and  the  difference  is  the 
barometric  height.  A  sufficient  quantity  of  the  liquid 
is  introduced  by  a  small  bent  pipette  for  there  to  be 
a  little  of  the  liquid  remaining  as  such  above  the  mer- 
cury. The  difference  of  the  new  heights  of  the  mercury 
inside  and  outside  now  represents  the  atmospheric 
pressure  minus  the  vapour  tension.  So  that  the  vapour 
tension  is  the  difference  between  the  first  pair  of  dif- 


Vapour  Tension.  47 

ferences  and  the  second.  This  would  be  exact  if  the 
liquid  were  only  just  but  completely  evaporated.  As, 
however,  to  ensure  saturation  of  the  vacuum  it  is  best 
to  allow  a  little  liquid  to  remain,  the  weight  of  this 
has  to  be  added  to  the  weight  of  the  internal  column  of 
mercury.  The  height  of  the  bottom  of  the  liquid  column 
may  be  taken  as  that  of  the  top  of  the  mercury  column. 
The  top  of  the  liquid  column  is  taken  as  the  lowest 
point  of  its  upper  surface.  To  translate  the  liquid 
column  pressure  into  mercury  pressure,  that  is,  to  find 
what  length  of  mercury  would  have  the  same  p1Gt 
downward  pull  as  the  observed  length  of 
liquid,  the  length  of  liquid  must  be  divided 
by  the  ratio  between  the  density  of  mercury 
and  the  density  of  the  liquid,  or  what  comes 
to  the  same  thing,  the  ratio  between  the 
specific  gravity  of  the  mercury  and  that  of 
the  liquid. 

§  53.  Let,  for  example,  a  barometer  tube  be  filled 
with  mercury  and  inverted. 

mm. 

Let  the  reading  of  the  mercury  inside  the 
tube  be  ......  780^2 

Let  the  reading  of  the  mercury  outside  the 
tube  be 30-5 

Then  the  barometric  height  (atmospheric 
pressure)  .  .  .  -=7497 

Let  a  liquid  be  now  introduced  which  has  the  specific 
gravity  of  0*872,  and  let  the  upper  surface  of  the  liquid 
stand  at  540-4  mm.,  the  lower  surface  of  the  liquid 
stand  at  535  -o  mm.,  the  inner  surface  of  the  mercury 


48  Practical  Physics. 

stand  at  535*0  mm.,  the  outer  surface  of  the  mercury 
stand  at  40*6  mm.  Then  inside  the  tube  there  are  535 
mm.  of  mercury  and  5*4  mm.  of  liquid.  The  "5*4 

mm.  of  liquid  are  equivalent  to  5*4x — ^—  mm.,    or 

0*3  mm.  of  mercury.  So  that  inside  there  are  535*3 
mm.,  and  outside  40*6  ;  so  that  the  mercurial  pressure, 
that  is,  the  difference  between  the  atmospheric  pres- 
sure and  the  vapour  tension,  is  4947  mm.  The 
atmospheric  pressure  being  749*7,  the  vapour  tension 
is  255*0  mm. 

How  vapour  tension  varies  with  temperature  will 
be  described  in  the  treatise  on  HEAT.  It  may  be 
here  mentioned  that  the  additional  elements  to  be 
taken  into  account  are  (i)  the  variation  in  density 
of  the  mercury  according  to  temperature,  and  (2) 
the  elongation  of  the  scale  if  it  be  etched  on  the 
glass. 

§  54.  The  vapour  tensions  of  solids  are  measured 
in  a  similar  manner.  In  order  to  avoid  the  irregularity 
of  the  mercury  surface  when  a  solid  rests  upon  it,  the 
barometer  tube  may  be  made  double,  and  one  limb 
FIG.  26.  being  graduated,  the  solid  is  introduced  into 
the  other.  This  form  of  barometer  is  indeed 
or  liquids  also  advantageous,  because  the 
liquid  being  introduced  into  one  limb,  the 
height  of  the  mercury  in  the  other  has  not  to 
be  corrected  for  the  liquid  column.  By  this 
means,  or  by  a  series  of  barometer  tubes  ar- 
ranged side  by  side,  it  is  easy  to  show  that  the  vapour 
tensions  of  saline  solutions  are  less  than  those  of 
water,  and  are  less  according  as  the  solutions  are 


Osmose.  49 

stronger.  Also  that  the  solid  water  in  crystalline  salts 
containing  water  of  crystallisation  has  various  vapour 
tensions,  while  the  water  in  solutions  however  strong 
of  gums,  glues,  or  other  colloidal  substances,  exerts 
the  same  vapour  tension  as  pure  water,  and  indeed 
that  the  water  in  gelatinised  colloid  solids  (jellies)  has 
precisely  the  same  vapour-tension  as  water  itself. 

§  55.  That  colloid  bodies  have  little  or  no  hold 
on  water  and  other  crystalloid  bodies  (the  terms  will 
be  more  fully  explained  in  §§  57,  58)  is  shown  very 
simply  on  placing  some  strong  solution  of  gum  arabic 
in  a  basin  under  the  receiver  of  a  good  air-pump.  On 
rapid  and  nearly  complete  exhaustion  being  effected, 
the  gum  boils  violently.  If  a  50  per  cent,  solution  of 
glue  be  placed  in  a  test  tube,  and  surrounded  with 
water  in  a  larger  tube,  the  glue  solution  boils  before 
the  water  if  the  latter  be  heated  very  gradually.  The 
glue  solution  boils  in  fact  at  97 '5°  C. 

§  56.  Diffusion  of  Liquids  into  Solids.  Osmose. — It 
seems  that  no  liquid  can  penetrate  through  a  crystalline 
solid  without  dissolving  it.  By  enormous  pressure 
water  can  be  forced  through  masses  of  iron  as  in  the 
cylinders  of  hydraulic  presses,  but  it  seems  from 
analogy  probable  that  the  water  passes  between  the 
crystals  of  iron  and  not  through  them.  Bodies  which 
as  solids  show  no  traces  of  crystalline  form  are  called 
amorphous,  their  fracture  is  conchoidal.  Such  bodies 
are  glass,  resin,  glue,  gum,  some  varieties  of  quartz, 
caoutchouc.  Such  of  these  as  are  soluble  in  liquids,  as 
gum  and  glue  in  water,  or  resin  in  alcohol,  may  or  may 
not  form  jellies  with  the  liquid.  Thus  gum  arabic  does 
not,  but  gelatine  on  being  heated  with  water  does, 
E 


5O  Practical  Physics. 

on  cooling,  form  a  jelly.  So  does  caoutchouc  with 
benzol.  A  jelly  appears  to  be  the  result  of  the  partial 
reaggregation  of  the  particles  of  the  colloid. 

Perhaps  melted  caoutchouc  and  fused  glass  may  be 
considered  to  be  colloid  liquids.  A  colloid  solid,  even 
when  insoluble  in  a  liquid,  may  and  often  does  allow 
that  liquid  to  penetrate  it,  but  it  does  not  allow  col- 
loids to  pass  through  with  anything  like  the  same 
facility.  The  passage  of  crystalline  solids  in  solution 
and  liquids  through  colloid  septa  is  properly  called 
osmose.  *  Vegetable  parchment'  or  '  parchment  paper' 
is  convenient  for  studying  osmose  (see  Appendix).  A 
glass  tube  about  i  in.  wide  and  2  in.  long  has  a 
piece  of  parchment  paper  tied  tightly  over  one  end. 
The  tube  is  then  weighed,  partly  filled  with  a  salt  solu- 
tion of  known  strength,  and  again  weighed.  It  is  then 
immersed  to  such  a  depth  in  distilled  water,  in  a  wide 
basin,  that  the  upward  and  downward  pressures  at  the 
parchment  surface  are  as  nearly  as  possible  equal. 
The  inner  vessel  gains  in  weight,  but  loses  in  salt. 
The  quantity  of  water  which  has  passed  inwards 
minus  the  quantity  of  salt  which  has  passed  outwards 
is  the  difference  of  the  first  and  second  weighings. 
The  absolute  quantity  of  saTt  which  has  passed  out- 
wards is  got  directly  by  evaporating  the  contents  of 
the  outer  vessel,  or  indirectly  by  evaporating  those  of 
the  inner  vessel,  and  subtracting  from  the  amount 
known  to  have  been  there  to  begin  with.  In  such 
rases  it  is  difficult  to  say  whether  there  is  an  exchange 
between  salt  and  water  or  between  salt  solution  and 
water.  But  the  balance  of  motion  is  in  favour  of 
the  water.  Thus,  if  a  bladder  be  used  about  4-5 


Dialysis.  5 1 

times  as  much  by  weight  of  water  passes  to  the  salt 
solution  as  of  salt  to  the  water,  if  the  salt  be  chloride 
of  sodium.  The  osmic  equivalents  of  other  salts  are 
determined  in  the  same  way.  But  the  osmic  equiva- 
lents depend  also  upon  the  nature  of  the  membranes. 
Bladder  gives  different  values  from  vegetable  parch- 
ment. 

§  57.  Dialysis. — The  difference  referred  to  above 
seems  to  depend  upon  the  power  which  the  membrane 
has  of  absorbing  one  or  other  liquid.  A  piece  of  bladder 
softens  and  swells  in  water,  but  hardens  and  shrivels 
in  alcohol.  Placed  between  water  and  alcohol,  the 
former  penetrates  it  and  diffuses  from  the  other  side 
into  the  alcohol,  while  little  alcohol  can  pass  the  other 
way.  Take  now  caoutchouc  instead  of  bladder ;  this 
softens  and  swells  in  alcohol,  but  is  almost  imper- 
meable to  water.  If  accordingly  a  caoutchouc  mem- 
brane separates  alcohol  from  water,  the  alcohol  will 
pass  through  and  little  or  no  water  will  return.  It  is 
thus  that  wine  strengthens  in  skins  and  bladders,  but 
weakens  in  caoutchouc  bags.  Water,  however,  passes 
in  some  quantity  through  caoutchouc.  A  toy  air-ball, 
for  instance,  if  completely  filled  with  water  and  per- 
fectly closed  will  go  on  losing  water  with  great  regu- 
larity for  weeks.  And  if  dry  air  be  passed  along  two 
tubes  joined  together  by  a  piece  of  caoutchouc  tubing 
which  is  immersed  in  boiling  water,  the  air  will  be 
found  to  be  no  longer  dry.  The  facility  with  which 
crystalloid  bodies  in  solution  pass  through  many  col- 
loid membranes,  and  the  hindrance  almost  amounting 
to  obstruction  which  the  same  membranes  present  to 
colloids,  render  the  separation  of  colloids  from  crys- 
E  2 


52  Practical  Physics. 

talloids  easy  in  cases  where  it  would  be  difficult  to 
effect  the  separation  by  other  means.  The  dialyser 
consists  of  a  sheet  of  parchment  paper  stretched  be- 
tween two  concentric  hoops  of  gutta-percha.  This  tabor 
which  may  be  rilled  with  a  mixture  of  gum  and  salt 
in  solution  is  floated  on  pure  water.  After  some 
days,  the  outer  water  being  removed,  scarcely  a  trace 
of  salt  is  found  in  the  tabor,  while  scarcely  a  trace  of 
gum  has  passed  out  of  it.  It  is  thus  that  the  metallic 
and  alkaloid  poisons  may  be  separated  from  the  col- 
loidal mucilage  of  the  contents  of  the  stomach,  while 
of  course  the  most  effective  nitration  accompanies  the 
dialysis. 

It  appears  that  the  oxides  of  iron,  tin,  aluminum, 
and  silicon,  are  or  may  be  colloidal,  and  may  be  then 
either  soluble  or  insoluble  in  water. 

§  58.  To  obtain  soluble  oxide  of  iron,  hydro- 
chloric acid  is  digested  with  freshly-precipitated  hy- 
drated  sesquioxide  of  iron  until  no  more  is  dissolved. 
Placed  in  the  dialyser,  hydrochloric  acid  alone  passes 
through,  leaving  the  oxide  of  iron  in  solution  in  water ; 
after  some  days  the  separation  is  complete.  The 
solution  is  very  apt  to  gelatinise,  and  will  not  again 
dissolve  by  adding  more  water  or  heating.  Solu- 
ble alumina  may  be  got  in  a  similar  way.  Soluble 
silica  is  prepared  by  adding  basic  silicate  of  soda 
(soluble  glass)  to  an  excess  of  hydrochloric  acid  and 
dialysing  as  above. 

§  59.  Transpiration  of  Gases  through  Capillary 
Tubes. — The  amount  (volume)  of  gas  which  passes  in 
a  given  time  through  a  tube  depends  upon  the  width 
and  length  of  the  tube,  upon  the  difference  of  pres- 


Transpiration. 


53 


sure  between  the  two  ends  of  the  tube,  upon  the  tem- 
perature of  the  gas  and  upon  its  density.  For  mea- 
surement, each  of  these  factors  must  in  turn  vary,  all 
the  rest  being  constant.  The  apparatus  of  most  general 
use  is  shown  in  fig.  27. 

Water  dropping  from  A  is  made  to  continually  over- 
flow the  funnel  tube  B  :  the  overflow  being  carried  away 

FIG.  27. 


by  c.  B  passes  air-tight  through  a  cork  in  the  mouth 
of  a  vessel  v,  and  dips  beneath  the  surface  of  the  water 
in  the  little  tube  D. 

The  gas  in  v  escapes  by  the  tube  E,  and  after 
being  dried  in  the  two  tubes  F  and  o,  passes  into  the 
tube  H,  the  lower  part  of  which  is  capillary,  and 
which  is  surrounded  by  a  vessel  to  hold  ice,  or  hot 


54  Practical  Physics, 

water,  or  paraffin,  &c.  Thence  the  gas  escapes 
through  i,  and  is  collected  in  the  tube  j,  which  is  con- 
stricted and  marked  at  j,  and  stands  in  an  overflowing 
vessel  K.  The  effective  pressure  on  the  gas,  that  is 
the  difference  between  the  pressures  at  the  two  ends, 
is  independent  of  the  barometric  pressure,  and  is 
measured  by  the  length  of  the  column  from  the  sur- 
face of  the  water  in  B  to  the  surface  in  D.  And  this 
length  remains  the  same.  The  rate  is  measured  by 
the  time  required  to  fill  the  vessel  j.  The  following 
facts  appear  from  experiment  :  (i)  The  time  required 
for  the  passage  of  a  given  volume  of  air  through  a 
capillary  tube  is  equal  to  the  sum  of  the  times  required 
for  the  passage  of  the  same  volume  of  air  through 
each  part  of  the  tube  taken  separately.  (2)  The  open- 
ing up  of  the  tube  into  spaces  where  the  resistance  is 
zero  and  its  je-entrance  into  the  capillary  does  not 
affect  the  rate,  provided  that  the  entire  length  of 
capillary  tube  remains  the  same.  (3)  Under  like 
conditions  the  same  passage  of  air  takes  place  down 
a  conical  capillary  tube,  whether  it  passes  from  the 
broad  to  the  narrow  end,  or  the  reverse.  (4)  The 
time  (resistance)  varies  approximately  as  the  square 
of  the  absolute  temperature,  that  is  the  temperature 
measured  from  — 273°  C.  (5)  The  time  varies  nearly 
exactly  inversely  as  the  pressure,  but  rather  more 
rapidly  than  that  reciprocal. 


Specific  Gravity.  55 

DENSITY,  COMPARATIVE  WEIGHTS  OF  EQUAL 
VOLUMES,  ABSOLUTE  WEIGHTS  OF  UNIT  VO- 
LUME, SPECIFIC  GRAVITY. 

§  60.  The  exact  methods  adopted  for  finding  the 
specific  gravities  of  bodies  vary  according  to  the  nature 
of  the  bodies.  We  will  consider  separately  the  fol- 
lowing cases  : 

Solids. 

1 i )  A  solid  in  lumps  not  less  than  a  hazel  nut,  in- 
soluble in  water,  (a)  heavier  than  water,  (b)  lighter 
than  water. 

(2)  A  solid  in  lumps  not  less  than  a  hazel  nut, 
soluble  in  water,  (a)  heavier  than  water,  (b)  lighter 
than  water. 

(3)  A  powder  insoluble  in  water,  (a)  heavier,  (/;) 
lighter  than  water. 

(4)  A  powder  soluble  in  water,  (a)  heavier,  (b) 
lighter  than  water. 

Liquids. 

(5)  A  liquid  to  be  had  in  considerable  quantities. 

(6)  Very  small  quantities  of  liquids. 

§  6 1.  A  balance  suitable  for  taking  specific  gravi- 
ties should,  when  loaded  with  50  grams  on  each  pan, 
show  the  effect  of  0*0002  gram.  Most  balances  are 
provided  with  a  short-slung  brass  pan  having  a  hook 
at  its  bottom.  This  brass  pan  is  sometimes  lighter 
and  sometimes  heavier  than  the  pan  on  the  other 
side.  If  lighter  it  is  best  to  add  a  chip  of  glass  or 
a  watch-glass  to  make  it  heavier.  It  is  not  advisable 
to  attempt  to  make  or  use  a  counterpoise.  Weights 


56  Practical  Physics. 

are  added  to  the  weight  pan  till  there  is  equilibrium, 
and  the  weight  so  added  has  to  be  deducted  from  all 
subsequent  weighings.  This  is  not  necessary  when  as 
in  (3),  (4),  (5),  (7)  and  (8)  an  apparatus  is  weighed 
along  with  the  substance  :  for  then  the  error  of  the 
balance  counts  as  weight  of  apparatus. 

The  most  usual  way  of  performing  the  determina- 
tion of  (i)  depends  upon  the  fact  that  a  body  totally 
immersed  in  water  is  buoyed  up  by  a  force  equal  to 
the  weight  of  water  it  displaces,  that  is  by  a  force  equal 
to  the  weight  of  water  having  a  volume  equal  to  the 
volume  of  the  body.  In  other  words,  the  weight  which 
a  body  loses  in  water  is  the  weight  of  water  whose 
volume  is  equal  to  its  own.  And  the  specific  gravity 
of  a  substance,  being  the  ratio  between  the  weight  of 
any  volume  of  the  substance  and  the  weight  of  an, 
equal  volume  of  water,  is*  got  by  dividing  the  weight  of 
the  body  by  the  weight  which  it  loses  in  water.  We 
may  here  neglect  the  buoying  effect  of  the  air  upon, 
the  body  and  the  weights. 

§  62.  As  an  example  of  (10)  we  may  take  quartz. 
A  watch-glass  placed  on  the  substance  pan  is  counter- 
poised by  4-3256  grams.  A  lump  of  quartz  is  placed 
on  the  watch-glass  and  the  two  require  57237. 
Accordingly,  weight  of  quartz  (in  air)  =  1-3981. 

The  quartz  is  tied  to  a  fibre  of  cocoon  silk  having 
a  loop  at  the  othei  end,  so  that  when  hanging  by 
the  loop  from  the  hook  of  the  substance  pan  the 
quartz  is  about  two  inches  from  the  bottom  of  the 
balance  (or  pan  support).  Being  so  hung  it  is  again 
weighed  (the  watch-glass  remains).  The  new  weight 
is  57244.  The  silk  fibre  weighs  therefore  0-0007. 


Specific  Gravity  of  Solids.  57 

Breathe  on  the  surface  of  the  quartz  and  hang  it  in  a 
vessel  of  distilled  water  of  such  a  width  that  the  quartz 
may  swing  freely,  and  of  such  a  height  that  about  half 
the  silk  is  immersed.  Any  air  bubbles  which  adhere 
to  the  quartz  are  teased  off  with  the  feather  of  a  pen. 
Let  the  weight  in  the  water  be  5*1270.  Since  the  silk 
fibre  has  very  nearly  the  same  density  as  water,  the 
part  immersed  does  not  affect  the  weight.  The  part 
outside  may  be  taken  as  0*0003,  so  that  5*1267  is  the 
weight  of  the  watch-glass  and  immersed  quartz.  And 
therefore  57237  —  5'i267  or  0*5970  is  the  weight  lost 
by  the  quartz,  that  is  the  weight  of  an  equal  volume 
of  water,  and  therefore 

1^81  or 
•5970 

is  the  specific  gravity  of  this  specimen  of  quartz. 

§  63  (i£).  To  find  the  specific  gravity  of  a  solid 
insoluble  in  water  and  lighter  than  water,  the  device  is 
employed  of  fastening  to  it  a  body  of  sufficient  weight 
to  sink  it.  Example  : 

§  64.  Let  it  be  required  to  find  the  specific  gravity 
of  paraffin.  Let  the  weight  of  the  paraffin  in  air  be 
4*2730.  A  piece  of  lead,  weighing  in  water  say  7*5964, 
is  stuck  to  the  paraffin.  The  two  together  weigh  in 
water  6*4236.  Accordingly  the  weight  lost  by  the 
paraffin  is  equal  to  the  weight  of  the  paraffin  in  air-f 
weight  of  lead  in  water  diminished  by  the  weight  oi 
both  together  in  water,  or 

=4*2730  + 7*5964-6-4236=5*4458. 
Therefore  the  specific  gravity  of  the  paraffin  is 


58  Practical  Physics. 

4^130  or  07846. 
5*4458 

§  65.  Solids  soluble  in  Water. — (20).  We  wish  to 
find  the  specific  gravity  of  a  salt  which  can  be  obtained 
in  pretty  large  crystals  like  rock-salt,  washing  soda  or 
alum.  A  piece  of  the  salt  is  found  to  weigh  5  -2 103 
grams  in  air.  Next  it  is  weighed  in  some  liquid  of 
known  specific  gravity  in  which  it  is  insoluble,  say  oil 
of  turpentine  of  specific  gravity  0*8742.  Let  its  weight 
in  turpentine  be  37020.  The  loss  in  weight  in  tur- 
pentine, that  is  the  weight  of  an  equal  volume  of  tur- 
pentine, is  1*5083.  What  is  the  weight  of  this  same 
volume  of  water  ?  Since 

sp.  gr.  of  turpentine  =  ^_ 

wt.  of  equal  vol.  of  water 

wtofanyvol.  of  turpentine  =  wt  of      ^  yo, 
sp.  gr.  ot  turpentine 

or  —I — ^  _  Wk  of  equal  voL  of  water 

0*8742 

=  17254 
And  therefore  the  specific  gravity  of  sal 

=  5^3  3. 

17254 

§  66.  (2^).  A  solid  lighter  than  water  and  soluble 
in  it.  Such  substances  are  rare ;  some  kinds  of 
shaving  soap  are  of  this  nature.  The  methods  of 
ib  and  20  are  combined.  That  is,  a  known  weight 
of  the  substance  is  weighted  with  a  sinker  whose 
weight  in  a  suitable  liquid  of  known  specific  gravity 
has  been  ascertained. 


Specific  Gravity  of  Liquids.  59 

Thus,  weight  of  soap  =5-7321  grams. 

,,        sinker  in  turpentine  =2  '4050     „ 
Let  weight  of  both  in  turpentine   =2  '4011 
.*.    wt.  of  turpentine  having  vol.  equal  to   soap 

=  5736o. 

/.   wt.    of   water    having    vol.    equal    to    soap 
5736o 
0-8742 

/.   sp.  gr.  of  soap  =  -5  ^2I  _.  0-8736. 
' 


§  67.  Before  considering  30,  3^,  40,  4^,  it  will  be  con- 
venient to  consider  liquids.  There  is  great  choice  in 
the  methods  which  can  be  here  adopted.  The  most 
convenient,  and  one  of  the  most  exact,  is  that  in  which 
the  specific  gravity  bottle  is  employed. 

(50.)  A  little  flask  capable  of  holding  about  30 
to  50  grains  of  water  has  a  rather  conical  stopper 
perfectly  ground  into  its  neck.  Through  the  stopper 
is  a  very  fine  hole  ;  the  stopper  may  be  made  of  a 
piece  of  thermometer  tubing.  The  F 

flask  is  weighed  empty.  Suppose 
its  weight  is  57230.  As  we  do  not 
require  to  know  the  absolute  weight 
of  the  flask  apart  from  inequality  of 
the  balance,  we  may  here  dispense 
with  the  preliminary  weighing  of 
§  6  1.  The  stopper  being  removed, 
the  flask  is  filled  by  a  pipette  with 
distilled  water  until  the  water  is  about  on  a  level  with 
the  edge.  With  the  exception  of  the  neck  it  is 
wrapped  lightly  in  a  soft  cloth,  and  being  held  by  the 


60  Practical  Physics. 

finger  and  thumb  by  the  neck,  and  held  a  little 
obliquely,  the  bottom  of  the  stopper  is  placed  in  con- 
tact with  the  water,  and  the  stopper  is  pressed  home 
uniformly,  not  too  quickly  and  without  a  grinding 
motion.  The  excess  of  water  is  so  squeezed  out, 
and  any  drop  remaining  on  the  top  and  about  the 
crack  between  the  neck  and  the  stopper  is  wiped  off, 
care  being  taken  not  to  warm  the  flask  and  especially 
not  to  press  in  its  elastic  bottom.  It  is  then  re- 
weighed.  Suppose  it  now  weighs  36*4723  grams. 
The  water  in  it  weighs  36*4723  —  57230  or  30-7493 
grams.  Let  the  water  be  emptied  out  and  the  flask 
thoroughly  dried,  first  by  shaking  and  then  by  warm- 
ing with  rapid  twirling  over  an  air-gas  burner  and 
drawing  air  out  of  the  flask  by  the  mouth  with  a  piece 
of  glass  tube.  When  thoroughly  cooled  it  is  to  be 
filled  with  the  liquid  as  before.  Its  weight  is  now 
found  to  be  say  38-4820.  The  liquid  in  it  accordingly 
weighs  38-4820  —  57230  or  32-7590,  and  the  specific 


gravity  of  the  liquid  is       _  _    !'C653.     This 

307493 

method,  it  is  clear,  is  equally  applicable  whether  the 
liquid  be  heavier  or  lighter  than  water.  The  flask 
maybe  more  rapidly  dried  if  it  be  rinsed  out  with 
alcohol  and  then  with  ether. 

§  68.  Another  method,  and  one  of  greater  rapidity 
and  almost  equal  accuracy,  is  to  weigh  a  conveniently 
shaped  lump  of  glass  suspended  from  the  short  scale 
pan  by  a  silk  fibre,  as  described  in  §  62,  and  then  to 
weigh  it  in  succession  in  air,  in  water,  and  in  the  liquid. 
Its  loss  of  weight  in  the  liquid  divided  by  its  loss 
of  weight  in  water  is  the  specific  gravity  of  the  liquid. 


Specific  Gravity  of  Powders.  61 

§  69.  Sometimes  only  very  small  quantities  of  the 
liquid  can  be  ob-  FlG.  29. 

tained.  A  piece  of 
light  tubing  (fig.  29) 
may  then  be  drawn 
out  at  both  ends  as  a  capillary  P.  The  tube  P  is  then 
used  exactly  like  the  specific  gravity  flask  of  §  67, 
being  weighed  empty,  full  of  water,  and  full  of  the 
liquid.  Liquids  which  cannot  be  drawn  into  the 
mouth  with  impunity  are  drawn  into  the  tube  P  by 
means  of  the  enveloping  tube  Q ;  the  end  R  is  placed 
in  the  mouth,  P  is  subsequently  removed,  and  the  two 
capillary  ends  wiped. 

§  70.  Occasionally  still  smaller  quantities  of  liquids 
are  at  our  disposal.  If  the  liquid  be  somewhat  heavier 
than  water  and  insoluble  in  it,  the  following  device 
may  be  sometimes  used  with  advantage.  A  drop  of 
the  liquid  is  placed  beneath  the  surface  of  a  small 
quantity  of  water,  and  a  saturated  solution  of  some  salt 
which  is  without  action  on  the  liquid,  is  added  with 
gentle  stirring,  till  the  drop  is  in  indifferent  equili- 
brium. The  specific  gravity  of  the  salt  solution  being 
taken  in  one  of  the  ways  described  above,  is,  of  course, 
identical  with  that  of  the  liquid  drop. 

§  71.  (30.)  A  powder  insoluble  in  and  heavier  than 
water.  The  specific  gravity  flask  is  weighed  empty, 
and  again  full  of  water ;  it  is  then  emptied,  dried, 
nearly  filled  with  the  powder,  and  weighed.  The 
powder  is  covered  with  distilled  water,  and  put 
into  the  air-pump  vacuum  to  remove  adhering  air; 
the  flask  is  then  filled  up  with  water  and  again 
weighed. 


62  Practical  Physics. 

Let 

Empty  flask  weigh  =  57230  .  .  w\ 
Flask  full  of  water  =36-4723  .  .  wz 
Flask  +  powder  =20-2356  .  .  ws 

Flask  +  powder  +  water  =40  -403  8  .        .  w4 
Then- 

Water  completely  filling  flask    =307493=  w2—Wi 
The  powder  weighs  =  14-5126=^3—^ 

Difference  between  weight  of 
powder  and  weight  of  equal 
vol.  of  water  = 


/.  Weight  of  water  having  same  vol.  as  powder 

=  10-5811=  wz—wl  —  (w4—  wz) 
/.  Specific  gravity 


10-5811 

§  72.  (3&)  If  tjie  powder  be  lighter  than  water  and 
insoluble  in  it,  the  flask  is  first  weighed  empty,  then 
full  of  water,  it  is  then  inverted  into  a  little  basin  of 
water,  and  a  quantity  of  the  powder  is  floated  up  into 
the  flask,  it  is  re-inverted,  dried,  and  weighed.  The 
water  being  evaporated  off,  the  flask  and  powder  are 
weighed  together.  The  data  are  as  in  30. 

§  73.  (40.)  Let  the  powder  be  heavier  than  water, 
but  soluble  in  it.    Proceed  as  in  30,  but  employ  some 
liquid,   say    turpentine,    of    known    specific    gravity 
(0*8742)  in  which  the  powder  is  insoluble. 
Let 

Empty  flask  weigh       .         .       5*7230  .         .  w\ 
Flask  full  of  turpentine        .     30-4723  .         .  iv2 


Vortex  Rings.  63 

Flask  +  powder  .         .         .     18-9379  .         .  w3 
Flask  +  powder  +  turpentine     32-4040  .         .  w4 

Then  w3—w\  —  (w^—w^  is  the  weight  of  turpentine 
having  vol.  equal  to  that  of  powder,  and  therefore 


3-2149-1-9317 


sp.  gr.  of  turpentine  0-8742 

is  the  weight  of  water  whose  vol.  is  that  of  the  powder, 
and  therefore  the  specific  gravity  of  the  powder  is 

5^'  ot   '3'»49  or  9-oo8. 
1-467  1-467 


VORTEX   MOTION. 

§  74.  As  a  connecting  link  between  ordinary  motion 
of  translation  of  fluids — air  and  water  currents — on  the 
one  hand,  and  the  motion,  which  gives  rise  to  waves, 
on  the  other,  stands  the  beautiful  phenomenon  of  vor  • 
tex  motion,  which  combines  both  kinds,  and  enables  a 
mass  of  fluid  to  travel  through  a  mass  of  fluid  with- 
out much  disturbance  to  the  latter.  Smoke  rings,  gun- 
ners' rings,  rings  following  FIG.  3o. 
the  spontaneous  ignition  in 
the  air  of  impure  hydride  of  -*—  g 
phosphorus,  and  occasion- 
ally steam  rings  from  loco- 
motives, are  familiar  ex- 
amples of  these.  They  can  be  conveniently  shown  on 
a  large  scale  by  replacing  the  back  of  a  box,  fig.  30,  by 
canvas  or  '  duck,'  cutting  in  the  front  a  circular  hole, 


64  Practical  Physics. 

which  should  have  a  sharp  edge  and  be  provided  with 
a  sliding  cover.  Two  flasks,  containing  respectively 
ammonia-water  and  hydrochloric  acid-water,  are  con- 
nected by  tubes  with  the  inside  of  the  box,  and  on 
being  heated,  fill  the  inside  with  clouds  of  chloride  of 
ammonium.  On  removing  the  cover  from  the  hole,  and 
hitting  the  canvas  back,  ring  after  ring  of  cloud-charged 
air  passes  out,  and  may  be  made  to  blow  out  a  candle  at 
ten  or  fifteen  yards.  On  sending  them  at  a  gentle  rate, 
and  examining  their  structure,  they  are  found  to  have 
an  internal  motion,  indicated  in  fig.  3 1  by  the  arrows, 
FIG.  31.  as  though  they  were  rings  of 

elastic  material,  rolling  in  tubes 
touching  and  exercising  friction 
on  their  circumferences.  A 
character  of  these  rings  is  that 
when  they  are  in  rapid  move- 
ment, general  and  internal,  they 
show  great  elasticity  one  towards  the  other,  in  fact,  it 
is  impossible  to  get  two  to  break  one  another. 

Similar,  but  imperfect,  liquid  vortex  rings  are  seen 
when  ink  is  dropped  gently  into  water.  They  are 
formed  in  great  beauty  as  fol  ows  :  a  round  side- 
chamber  is  fastened  to  the  end 
of  a  long  trough  having  glass 
sides.  The  side-chamber  com- 
municates with  the  trough  by  a 
circular  opening  rather  less  than 
the  chamber.  The  other  end  of  the  chamber  is 
covered  by  a  stout  piece  of  vulcanised  caoutchouc. 
The  trough  and  chamber  are  filled  with  clear  water,  a 
little  colouring  matter  is  put  into  the  water  in  the 


Waves.  65 

chamber  by  means  of  a  pipette.  The  caoutchouc  is 
struck  by  a  round-headed  mallet,  or  thrust  in  by  a 
lever  attached  to  the  trough,  resembling  a  'lemon 
squeezer.'  If  sulphate  of  indigo  is  used  as  a  colouring 
agent,  the  water  soon  clears  itself  if  it  holds  some 
hypochlorite  of  lime  in  solution,  and  so  the  trouble  of 
refilling  is  avoided 


WAVES. 

§  75.  The  wave  in  general.  —  Conceive  a 
number,  n,  of  particles,  exactly  alike  one  another, 
and  arranged  in  a  straight  line  at  equal  distances, 
say  one  inch  apart.  Let  the  particles  be  called 
a,  t>,  c,  d,  e,  &c.  Let  the  particle  a  move  in  any 
way,  but  come  back  to  its  original  place  in  the  time 
10  seconds.  Suppose  that  b  starts  i  second  after 
a,  and  performs  a  path  just  like  a's  path.  Let  c  start 
i  second  after  b,  let  d  start  i  second  after  c,  and  so 
on  ;  each  particle  completing  its  course  in  the  same 
time,  10  seconds,  and  these  courses  being  identical  in 
size  and  shape,  but  differing  in  position,  because  the 
starting  points  are  i  inch  apart.  Suppose,  now,  that 
when  a  has  come  back  to  its  original  position,  that  is, 
after  10  seconds,  the  particle,  £,  which  is  10  inches 
from  a,  just  begins  to  stir.  The  particle,  #,  has  been 
moving  for  10  seconds,  and  has  completed  \%  of  its 
course,  the  particle  b  has  been  moving  for  9  seconds, 
and  has  completed  T%  of  its  course,  and  so  on ;  the 

F 


66  Practical  Physics. 

particle  j  has  been  moving  i  second,  and  has  com- 
pleted ^  of  its  course,  the  particle  k  is  just  about  to 
move  or  just  moving,  and  has  completed  nothing,  or 
an  infinitely  small  fraction  of  its  course.  Let  now  (at 
the  end  of  10  seconds)  a  start  afresh  as  before,  and 
next  £,  and  then  <:,  and  so  on,  each  starting  always 
afresh  as  soon  as  it  gets  home.  It  is  clear  that  during 
the  next  10  seconds,  and  ever  afterwards,  a  and  k 
will  be  moving  alike,  and  be  in  similar  positions,  so 
will  b  and  /,  c  and  ?;z,  d  and  ;/,  and  so  on. 

The  distance  from  a  to  k,  or  from  b  to  /,  or  from 
c  to  m,  &c.,  always  in  our  case  10  inches,  is  the 
wave's  length.  Wave-length  is  the  distance  between 
any  one  particle  and  the  next  particle  which  has 
completed  the  same  fraction  of  its  course  as  the  first 
one  has  completed  :  this  is  called  being  in  the  same 
phase. 

The  greatest  difference  in  the  positions  of  one 
and  the  same  particle  is  called  the  wave's  amplitude. 

A  wave  is  accordingly  a  travelling  condition  of 
matter  in  regard  to  the  position  of  its  particles. 

It  follows  from  the  example  that  the  travelling 
condition  has  passed  from  a  to  k  in  the  same  time  as 
sufficed  to  bring  a  back  to  its  original  position ;  and 
universally,  a  wave  travels  its  own  length  in  the  same 
time  as  that  in  which  any  particle  completes  an  entire 
course. 

§  76.  Waves  governed  by  gravity.  Liquid  waves. 
—These  are  familiar  as  water  waves.  The  actual 
motions  of  the  individual  particles,  which  motions 
produce  the  water  wave,  can  be  seen  if  we  employ  a 
long  trough  of  water  with  glass  sides,  and  float  a  wax 


Water   Waves.  67 

pellet  slightly  loaded  with  sand,  so  that  it  only  just 
floats  in  the  water,  near  to  the  glass  side.  A  paddle, 
nearly  fitting  the  trough,  is  placed  about  6  in.  from 
one  end,  and  advanced  about  J  in.  towards  the  wax, 
and  immediately  afterwards  back  again.  This  gives 
rise  to  a  travelling  elevation,  followed  by  a  travelling 
depression;  these  dandle  the  wax  pellet,  and  it  is  seen 
to  describe  a  circle.  If  the  wave's  motion  is  said  to 
be  one  of  advance,  the  pellet  rises  advancing,  then 
sinks  advancing,  then  sinks  retreating,  then  rises  re- 
treating. The  first  two  parts  of  the  motion  are 
due  to  the  wave's  elevation,  the  latter  to  its  valley. 
In  such  a  wave  each  particle  describes  a  nearly 
circular  orbit  in  a  vertical  plane  which  lies  in 
the  direction  of  the  wave's  motion.  The  wave- 
length is  from  top  of  crest  to  next  top  of  crest, 
a  to  b,  or  from  bottom  of  valley  to  next  bottom  of 
valley,  c  to  d,  FlG-  33- 

or   from   any  /^T**?  -V^Nf  / 

particle,  e,  in ,/^    i     >. — -/- — — ^~ — -^— 

any  phase,  to  cr         £ —  d 

the  next  particle,  f,  in  the  same  phase.  It  is  clear 
that  particles  at  the  same  height  are  not  necessarily 
in  the  same  phase.  The  particles  e  and  g,  for  in- 
stance, are  at  the  same  height,  but  one  is  going  down 
while  the  other  is  going  up.  The  amplitude  is  the 
length  of  the  line  a  ^,  or  the  vertical  distance  between 
the  top  of  a  crest  and  the  bottom  of  a  valley. 

§  77.  Reflexion  of  water  waves.     Stationary 

waves. — If  the  wave  generated  in  the  trough  of  §  76 

be  watched  as  it  strikes  the  end  of  the  trough,  it  is 

seen  that  the  elevation  is  reflected  as  an  elevation, 

F  2 


68  Practical  Physics. 

and  the  depression  as  a  depression,  also  that  the  height 
to  which  the  wave  rises  and  the  depth  to  which  the 
valley  sinks  on  reflexion  are  about  double  the  original 
wave  height.  If  we  use  a  shorter  trough,  we  can  start 
a  fresh  wave  of  such  a  length  and  at  such  a  moment 
that  the  beginning  of  the  advancing  valley  of  the 
second  wave  meets  the  beginning  of  the  reflected 
elevation  of  the  first  wav'e  in  the  middle  of  the  trough. 
FlG  34  The  line  of  particles  across  the  mid- 

dle of  the  water  surface  will .  then 
always  be  urged  upwards  and  down- 
wards by  the  same  pressure,  and 
will  not  vary  in  height,  and  the 
water  will  rise  at  a  and  fall  at  b,  and  vice  versa  simul- 
taneously. The  particles  at  a  and  b  are  always  in 
opposite  phases,  and  therefore  a  and  b  are  half  a  wave- 
length apart,  or  the  wave-length  is  double  the  trough's 
length.  The  systems  of  swayings  to  and  fro  in  this 
and  similar  cases,  are  called  'stationary'  waves.  The 
line  through  n  is  a  nodal  line.  With  regard  to  the 
actual  motion  of  the  water  particles  in  such  cases, 
suspended  wax  pellets  show  that  the  actual  motion  at 
the  reflecting  faces  is  vertical,  and  that  there  the  motion 
is  greatest.  At  the  node,  particles  sweep  through  it  in 
arcs,  without  altering  its  height.  All  the  other  parti- 
cles also  move  in  arcs  of  lesser  amplitude  as  they  lie 
deeper,  until  at  a  depth  of  about  a  wave-length  the 
movement  is  inappreciable.  If  the  trough  be  of  a 
lesser  depth,  the  friction  on  the  bottom  retards  the 
wave's  motion.  The  water  in  a  trough  can  be  set 
in  motion  in  a  variety  of  ways ;  thus,  if  the  centre 
be  depressed  and  released,  two  nodal  lines  will  be 


Stationary  Liquid   Waves.  69 

formed,  each  at  \  the  trough's  length  from  the  ends. 
The  wave  here  is  half  as  long  as  in  the  FlG>  35. 

former  case,  or  the  wave-length  is 
equal  to  the  trough's  length.  If  we 
count  the  number  of  times  an  eleva- 
tion appears  in  the  middle  in,  say, 


five  minutes  with  the  binodal  system,  and  also  with 
the  mononodal,  we  find  that  with  the  same  trough 

number  with  binodal       _  \/2 
number  with  mononodal  "~     i 

rate  of  progression 
length  of  path 

calling  rate  of  progression  of  binodal  rz 

„  „        mononodal  r* 

length  of  path  of  binodal  72 

„  „       mononodal  /,  (=2/2) 


2/2 

or  r±  =  v/7. 

rz 

Or  if  the  length  of  one  wave  is  twice  as  great  as  that 
of  a  second,  the  first  will  move  faster  than  the  second, 
in  the  ratio  of  \/2  :  i. 

§  78.  Such  waves,  in  rectangular  troughs,  are  how- 
ever restrained,  and  do  not  move  so  swiftly  as  when 
in  open  water,  or  when  reflected  from  the  sides  of 
circular  troughs.  The  connection  between  wave-length 
and  rate  of  wave  progression  is  practically  exhibited 


70  Practical  Physics. 

as  follows  :  two  cylindrical  troughs,  which  should  be 
at  least  as  deep  as  they  are  wide,  are  nearly  filled 
with  water  ;  the  bottom  of  an  empty  beaker  glass  is 
alternately  pressed  down  and  raised  in  the  centre  of  the 
water  of  one  of  them.  With  a  little  practice  the  hand 
and  water  help  one  another.  The  beaker  is  with- 
drawn, and  the  surface  allowed  to  free  itself  from 
ripples.  The  water  is  then  found  to  be  in  the  follow- 
ing kind  of  motion.  It  sinks  in  the  middle  zs  it  rises 
at  the  circumference,  and  vice  versd,  and  the  central 
motion  is  about  twice  as  much  as  the  circumferential. 
At  almost  exactly  ^  of  the  radius  from  the  circum- 
FIG.  36.  ference  there  is  a  nodal  ring.  Such  motion 
will  continue  for  ten  or  fifteen  minutes  in 
troughs  of  about  2  ft.  diameter.  The 
position  of  the  nodal  ring,  and  the  ampli- 
tude of  the  motion,  can  be  measured  by 
dipping  a  sheet  of  sized  paper  into  the  water  in  a 
vertical  plane  along  a  diameter. 

If  we  count  how  many  times  the  elevation  appears 
in  the  middle  in  a  given  time,  we  find  (i)  that  whether 
the  undulation  is  vigorous  or  nearly  expired,  the  same 
number  of  reappearances  occur  in  exactly  the  same 
time,  and  secondly,  if  the  diameter  of  the  trough  A  is 
dM  and  that  of  B  is  */b,  then  if  Na  be  the  number  of 
reappearances  in  a  given  time  with  A,  and  Nb  those 
with  B,  we  find  experimentally 


Now,  as  before,  the  number  of  reappearances  of  the 
crest  in  the  middle  varies  directly  with  the  rate  of 


Rate  of  Progression  of  Waves.          ?l 

progression  of  the  wave  and  inversely  with  its  length 
of  path.  The  path  is  in  both  cases  twice  the  respec- 
tive radius,  that  is,  it  is  the  respective  diameter. 
Calling  ra  the  rate  of  progression  in  A,  and  vb  that 
in  B,  we  have  therefore 

!> 

Nq  ffq   _    'V4 


or  the  rates  of  progression  are  directly  proportional  to 
the  trough  diameters,  that  is  to  the  wave-lengths.  It 
appears  from  experiments  of  this  nature  that  a  wave 
i  meter  in  length  will  travel  in  open  water  almost 
exactly  83  meters  in  a  minute,  or  about  3  miles  in  an 
hour.  Of  course  in  open  water  the  moving  water  has 
to  set  a  larger  and  larger  ring  of  water  in  motion  as 
the  circle  increases.  The  wave  loses  in  amplitude  as 
it  spreads.  It  also  appears  to  gain  a  little  in  length, 
The  latter  point  requires  examination. 

The  rate  of  recurrence  of  the  same  phase  in  the 
same  place,  which  may  be  called  the  rate  of  pulsation, 
depends  of  course  on,  and  is  the  same  as,  the  rate  of 
swing  to  and  fro  of  each  particle.  Each  particle  is 
virtually  a  pendulum,  but  only  those  symmetrically 
situated  move  in  equal  or  indeed  similar  arcs.  Still 
the  same  relationship  exists  with  the  wave  as  with  the 
pendulum  ;  for  the  rate  of  swing  of  the  latter  also4  that 


72  Practical  Physics. 

is,  the  number  of  times  of  its  reappearance  in  the  same 
phase  in  the  same  place,  is  inversely  as  the  square  root 
of  its  length.  The  relationship  is  still  more  close.  If 
a  pendulum  be  taken  whose  vibrating  length  is  exactly 
the  radius  of  the  circular  trough,  the  pulsating  water 
and  the  swinging  pendulum  will  keep  exact  time  with 
one  another  if  the  swing  of  the  pendulum  be  small. 
Further,  all  liquids  give  rise  under  like  conditions  (of 
wave-length)  to  waves  which  travel  at  the  same  rate 
whatever  be  the  densities  of  the  liquids  :  just  as  all 
pendulums  swing  at  the  same  rate  whatever  be  their 
weight,  if  they  are  of  the  same  length. 

§  79.  Waves  governed  by  elasticity. — In  all  other 
wave  systems  the  elasticity  of  the  matter  in  which  the 
wave  travels  takes  effect,  for  in  all  other  systems 
change  of  volume  accompanies  the  wave  in  its  motion. 
This  is  true  as  well  when  a  wave  of  transverse  dis- 
placement travels  along  an  elastic  rod  or  cord  as  it 
obviously  is  when  the  particles  move  in  succession  to 
and  fro  longitudinally,  that  is,  in  the  same  direction  as 
the  wave  itself  moves,  either  in  solids,  liquids,  or  gases. 

In  the  latter  case  indeed  the  wave  may  well  be 
called  a  wave  of  change  of  density;  and  as  elasticity 
varies  with  density,  it  may  also  be  called  a  wave  of 
elasticity.  Such  waves  travel  so  fast  that  their  rate  of 
motion  can  only  be  got  at  either  directly  by  taking  great 
lengths  of  them,  or  indirectly  by  finding  the  ^number 
of  recurrences  of  the  same  phase  in  a  given  time.  And 
this  is  again  generally  measured  by  the  varying  physio- 
logical effect  on  the  perception  when  the  drum  of  the 
ear  receives  various  numbers  of  pushes  and  pulls  in 


Waves  of  Elasticity.  73 

a  given  time,  and  so  communicates  sensations  of 
notes  of  different///^,  that  is,  shriller  or  graver  notes. 
Perhaps  the  simplest  conception  of  the  formation 
of  an  air  wave  system  from  a  solid  is  to  imagine 
a  sphere  surrounded  by  air,  and  to  suppose  the 
sphere  to  swell  and  shrink  alternately, — alternating 
spherical  concentric  shells  of  condensation  and  rare- 
faction would  be  thrown  off.  All  particles  at  the 
same  distance  from  the  sphere  would  be  in  the  same 
phase  at  the  same  time.  As  a  result  of  experiment  it 
is  found  that  at  the  end  of  the  first  second  the  first 
shell  would  be  at  1,100  feet  from  the  sphere,  and  there 
would  be  as  many  shells  of  compression  as  the  num- 
ber of  times  the  sphere  had  swollen  during  the  second. 
Alternating  with  these  would  be  as  many  spherical 
shells  of  rarefaction.  Each  air  particle  moves  fro  and 
to  as  it  takes  part  in  the  wave  motion,  in  a  straight  line 
radial  to  the  shells.  A  particle  begins  to  move  when 
the  front  of  the  shell  of  compression  touches  it,  and 
it  completes  its  motion  when  the  back  of  the  next 
shell  of  rarefaction  leaves  it.  Accordingly,  an  air 
wave,  like  a  water  wave,  travels  its  own  length  in  the 
time  that  a  particle  occupies  in  going  through  all  its 
changes  of  position,  so  as  to  be  ready  to  start  again  in 
the  same  direction.  The  length  of  an  air  wave  is  the 
distance  between  any  two  particles  in  the  same  phase : 
from  one  place  where  there  is  maximum  density  to 
the  next,  or  from  one  place  of  minimum  density  to  the 
next,  or  from  any  other  place  of  given  density  to  the 
next  but  one.  There  is  thus  a  very  great  analogy  be- 
tween an  air  or  sound  wave  and  a  water  wave,  as  fig.  37 


74 


Practical  Physics. 


shows,  where  in  (i)  the  closeness  of  the  lines  repre- 
sents the  closeness  of  the  particles  of  air  which  are 
made  to  correspond  with  the  elevations  and  depres- 
sions in  (2)  which  represents  wave  system  of  elevation 
and  depression.  It  is  clear  that  if  all  air  waves  travel 
at  the  rate  of  1,100  feet  a  second,  and  there  are  n  waves 
started  in  a  second,  the  whole  air  space  within  a 
radius  of  i, TOO  feet  will  at  the  end  of  a  second  consist  of 
n  shells  of  condensation  alternating  with  n  shells  of  rare- 
faction all  at  equal  distances  apart.  In  other  words, 

FIG.  37. 


NX       N^ 


there  will  be  n  waves  in  a  radius  of  1,100  feet.    Each 


i  TOO 


wave  will  be  therefore feet  long  and  universally 


wave-length  in  feet= 


no.  of  feet  wave  travels  in  i  second 
no.  of  waves  generated  in  i  second. 


The  amplitude  of  an  air  wave  is  the  greatest  dis- 
tance between  two  positions  of  one  and  the  same 
particle.  The  vis  viva  of  the  air  wave  has  to  be 
exerted  on  a  greater  and  greater  mass  as  the  wave 
spreads,  and  accordingly  the  amplitude  diminishes. 
Air  waves  are  audible  when  the  amplitude  cannot  be 


more  than 


10,000,000 


of  an  inch.    A  system  of  scund 


Notes.  75 

waves  slightly  increases  in  wave-length  as  the  wave 
radiates. 

§  80.  Conversion  of  sounds  into  Notes. — Without 
entering  upon  the  anatomy  and  physiology  of  the 
ear,  we  may  assume  that  an  elementary  sound  is  pro- 
duced by  a  single  air  wave  thrusting  in  and  pulling  out 
the  drum  of  the  ear.  The  duration  in  time  of  this 
excursion  is  the  same  as  that  of  the  excursion  of  any 
air  particle.  The  extent  of  the  drum's  excursion  de- 
pends upon  the  vigour  (vis  viva)  of  the  blow  it  receives 
(\  mv*}.  And  the  loudness  of  the  sound  is  not  ne- 
cessarily proportional  to  the  vigour  of  the  blow,  nor 
to  the  extent  of  the  drum's  excursion.  Sounds  are 
seldom  simple  in  their  origin,  and  even  when  they  are 
so,  echo  and  the  reverberation  of  surrounding  bodies 
generally  prolong  the  sound  and  alter  its  character. 
But  even  a  single  air  wave  produces  a  sensory  effect 
which  endures  after  mechanical  action  has  ceased  for 
a  time  of  about  -^  of  a  second.  If  a  second  similar 
sound  is  produced  within  this  time  interval,  the  sen- 
sations of  the  old  and  new  sounds  are  continuous.  If 
other  similar  waves  succeed  at  the  same  small  intervals, 
a  continuous  sound  is  produced,  called  a  note.  The 
quicker  the  sequence,  the  shriller  the  note,  the  higher 
its  pitch :  the  slower  the  sequence,  the  graver  the  note, 
the  lower  its  pitch.  A  large  humming-top  has  a  round- 
headed  nail  driven  into  its  peg.  The  lower  part  of 
the  upper  stem  is  cut  into  a  triangular  prism,  the  upper 
part  being  thinned.  Three  circular  discs  of  tin-plate 
have  triangular  holes  in  their  centres,  so  as  to  fit  on 
to  the  stem.  One  of  these  has  two  rings  of  holes,  the 


?6  Practical  Physics. 

outer  being  twice  as  numerous  as  the  inner.    The 
FlG  38  two  other  discs  are  toothed, 

the  larger  having  twice  as 
many  teeth  as  the  smaller. 
The  two  can  be  placed  to- 
gether  on  the  stem,  the  larger 
being  below  and  the  two 
being  separated  by  a  triangu- 
lar washer.  The  top  is  filled 
with  wet  sand,  and  the  hole 
stopped.  The  single  perforated  disc  being  slipped 
on  the  top  is  spun  in  the  usual  way  on  the  bottom  of 
a  tumbler.  Air  is  blown  upon  the  two  rings  of  holes 
in  succession  through  a  glass  tube,  the  bent-down  end 
of  the  tube  being  held  as  near  as  possible  to  the  disc 
without  touching  it.  A  puff  of  air  passes  through  each 
hole  as  it  comes  beneath  the  tube,  and  this  momen- 
tary air-puff  reaches  the  ear  as  a  sound-wave.  The 
puffs  succeeding  one  another  with  greater  rapidity  than 
1 6  in  a  second,  a  continuous  note  is  heard  which  for 
the  same  ring  of  holes  becomes  graver  as  the  top 
languishes,  but  is  always  for  the  outer  ring  an  octave 
higher  than  for  the  inner  ring.  So  when  the  two 
toothed  rings  are  put  on  and  the  top  spun,  a  card  held 
in  contact  with  the  twice  as  numerously  toothed  disc 
gives  always  the  note  which  is  the  higher  octave  of 
that  given  by  the  other  disc.  Both  become  graver  as 
the  rate  fades.  Hence  it  follows  not  only  that  a 
higher  pitched  note  is  the  result  of  more  frequent 
sound  waves  in  the  same  time  (and  therefore  shorter 
waves),  but  that  what  is  known  in  music  and  re- 
cognised by  most  ears  as  the  relation  between  a  note 


Sensitive  Flame.  77 

and  its  higher  octave  is  the  relationship  between  the 
impressions  which  n  and  zn  sound  waves  in  the  same 
space  of  time  make  upon  the  perception,  or  the  re- 
lationship between  the  impression  which  a  series  of 

sound  waves  of  length  /  and  a  series  of  length  -  make 

upon  the  perception.  Whether  the  feeling  called 
pitch  depends  upon  the  appreciation  of  the  rapidity 
of  sequence  or  upon  the  duration  of  each  distortion 
of  the  ear-drum  is  not  easy  to  decide,  for  the  one  is 
the  inverse  of  the  other.  Perhaps  the  fact  that  a 
single  long  wave  produces  a  different  impression  from 
that  produced  by  a  single  short  wave,  and  that  this 
difference  reminds  one  of  the  differences  between  grave 
and  shrill  notes,  may  be  regarded  as  evidence  that 
duration  of  individual  impression  rather  than  rate  of 
sequence  is  to  be  considered  as  the  origin  of  pitch. 

§  8 1.  Detection  of  sound.  Sensitive  flame. — In 
order  to  render  visible  facts  connected  with  the  re- 
flexion, refraction,  absorption,  and  dispersion  of 
sound,  use  is  made  of  the  effect  of  the  sound  wave  on 
fluid  jets.  Three  kinds  of  jets  are  used.  A  liquid 
pouring  in  a  smooth  vertical  jet  from  a  cistern  at  such 
a  slow  rate  that  it  is  ready  to  break  up  into  drops, 
will  so  break  up  if  subjected  to  sonorous  vibrations. 
A  jet  of  air  rendered  visible  by  being  charged  with 
smoke  becomes  stunted  under  the  same  conditions. 
Perhaps  the  most  striking  and  convenient  is  the 
sensitive  flame.  Coal  gas  is  collected  in  a  mackintosh 
bag  provided  with  a  stop-cock.  The  bag  is  placed 
between  boards,  which  are  so  loaded  that  the  elasticity 
is  increased  by  about  ^th  part.  The  gas  is  led  to  a 


78  Practical  Physics. 

long  straight  burner,  having  an  orifice  of  about  ^Vth 
of  an  inch.  This  will  give  a  flame  about  a  foot  high 
and  \  in.  diameter.  The  stop-cock  is  turned  on 
till  the  jet  is  on  the  point  of  '  flaring.'  Most  sounds 
and  notes  will,  when  not  too  far  from  the  flame,  cause 
it  to  duck  down  and  flare.  This  is  especially  the 
case  with  sibilant  sounds — hissing,  crumpling,  rustling, 
clinking,  scraping,  &c.,  all  of  which  sounds  consist  of 
or  contain  high  notes.  Notes  which  are  so  high  as 
to  be  inaudible  to  the  ear  affect  the  flame.  For  the 
flame  to  be  affected  it  is  necessary  that  if  the  jet  be 
of  rigid  material,  the  orifice  of  it  should  be  exposed 
to  the  beat  of  the  waves. 

.  §  82.  Reflexion  of  sound. — Let  a  sensitive  flame 
be  placed  at  one  end  of  a  metal  tube  1 2  feet  long  and 
a  few  inches  in  diameter.  Remove  the  pea  from  a 
dog-whistle,  and  sound  the  whistle  at  a  distance  of 
1 2  feet.  If  the  flame  respond,  diminish  the  supply  of 
gas  till  it  ceases  to  do  so.  Then  bring  the  sounding 
whistle  towards  the  other  end  of  the  metal  tube.  As 
it  gets  near  the  end,  it  will  cause  the  flame  to  duck 
and  flare,  and  when  it  is  on  the  axis  of  the  tube  it 
may  be  some  feet  from  it  without  ceasing  to  cause 
the  same  effect.  Diminish  the  sensitiveness  of  the 
flame,  so  that  when  the  whistle  is  sounded  at  the  other 
end  of  the  tube  the  flame  remains  tranquil.  Place  be- 
hind the  whistle  a  parabolic  or  spherical  mirror,  so  that 
the  whistle  is  in  the  principal  focus  and  the  axes  of  the 
tube  and  mirror  coincide.  The  flame  again  flares. 
Place  a  cloth  between  the  whistle  and  the  mirror,  the 
flame  is  restored.  To  exhibit  the  law  of  reflexion  of 
sound,  namely,  that  the  angles  of  incidence  and  re- 


Reflexion  and  Absorption  of  Sound.       79 

flexion  are  equal,  and  that  the  incident  beam,  the 
reflected  beam,  and  normal  to  the  surface  at  the  place 
of  incidence,  are  all  in  one  plane,  arrange  two  metal 
tubes,  each  about  4  feet  long,  horizontally  (fig.  39), 
and  at  right  angles  to  one  FlG  39< 

another.  Sound  the  whistle, 
w,  and  regulate  the  gas  so  that 
the  flame,  sf,  is  not  affected. 
Then  introduce  at  a  a  sheet  of 
cardboard  inclined  at  45°  to  «~ 

each  tube ;  the  flame  flares.  The  hand  placed  at  a 
also  reflects  the  sound  waves  to  sf.  The  flame  of  a  flat 
fishtail  burner  produces  the  same  effect,  and  so  does 
even  the  sheet  of  heated  gas  from  such  a  flame  when 
the  burner  is  placed  somewhat  lower  down. 

The  absorption  of  sound  is  exhibited  in  a  similar 
manner.  The  tubes  are  now  placed  in  the  same 
straight  line,  with  their  ends  about  an  inch  apart. 
The  whistle  is  sounded  uni- 
formly, and  the  flame  is  so 
adjusted  that  it  responds 
freely.  A  sheet  of  cardboard 
or  paper,  or  a  flat  gas  flame 

at  a,  cuts  off  the  sound  by  reflexion.  A  single  fold  of 
a  wet  towel  produces  the  same  effect ;  while  several 
folds  of  a  dry  towel  fail  to  cut  off  the  sound.  The 
films  of  water  in  the  wet  towel  being  of  different  sizes, 
break  up  the  waves  they  receive  into  waves  of  different 
sizes,  and  urge  them  in  different  directions.  Through 
the  dry  towel  the  air  is  continuous,  and  part  of  the 
wave  proceeds  unbroken. 

Perhaps    the    most    complete    arrangement    for 


8o  Practical  Physics. 

showing  most  facts    connected  with  reflexion   and 
FlG.  4I.  absorption,     disper- 

sion, &c.,  is  shown 
in  fig.  41,  where  two 
spherical  mirrors, 
about  18  in.  in  dia- 
meter, are  placed 
with  their  axes  in  one  line,  at  a  distance  of  about 
4  feet.  The  whistle  is  supported  in  the  principal  focus 
of  the  one,  and  -the  sensitive  flame  in  that  of  the 
other  (the  distance  of  the  principal  focus  from  the 
mirror  is  half  the  radius  of  the  mirror,  and  it  is 
measured  once  for  all  by  finding  where  the  image  of 
the  sun,  or  of  a  gas  flame  at  a  distance  of  20  or  30 
yards,  is  formed  on  a  transparent  paper  screen). 
The  flame  is  so  adjusted  that  without  the  mirrors  no 
effect  is  produced;  also  when  only  one  mirror  is  in 
position.  When  both  mirrors  are  in  position  the  flame 
flares.  This  flaring  is  not  prevented  by  placing  a 
2-inch  square  screen  between  w  and  sf,  however 
close  it  may  be  put  to  either ;  but  on  placing  it  close 
to  w,  between  w  and  its  mirror,  or  close  to  sf,  between 
sf  and  its  mirror,  the  flame  ceases  to  flare.  The 
actual  tracing  of  the  sound-wave  before  and  after 
FIG.  42.  reflexion  is  shown  by  the 

device  in  fig.  42.  A  per- 
fectly flat  and  very  smooth 
elliptical  board,  japanned, 
is  surrounded  by  a  smooth 
wall  2  or  3  inches  high,  the  axes  of  the  ellipse  being  as 
three  to  four.  Two  brass  knobs  are  fastened  above  the 
board  about  J  in.  apart,  in  such  a  way  that  the  straight 


Refraction  of  Sound.  81 

line  joining  them  is  bisected  by  one  focus  of  the  ellipse. 
Dry  lycopodium  is  scattered  through  muslin  uniformly 
over  the  wood,  and  the  whole  is  covered  by  a  glass 
plate.  One  of  the  knobs  is  connected  with  the  inner 
coating  of  a  Leyden  jar,  the  other  with  the  outer 
coating  and  the  earth.  The  inner  coating  of  the  jar 
is  also  connected  with  the  prime  conductor  of  an 
electrical  machine.  On  turning  the  machine,  sparks 
pass  from  knob  to  knob,  giving  rise  to  sound  waves. 
These  waves  are  reflected,  and  converge  to  the  other 
focus.  The  lycopodium  is  found  to  be  arranged  in 
two  families  of  concentric  circles  around  the  foci. 
Strictly  speaking,  we  do  not  get  here  a  tracing  of  a 
moving  wave ;  for  a  moving  wave  can  leave  no  tracing 
of  accumulation,  because  each  particle  moves  equally 
in  its  turn.  What  we  find  is  the  tracing  of  a  system 
of  stationary  waves,  due  to  the  interference  of  the 
echo  waves  with  the  original  waves. 

§  83.  Refraction  of  sound. — As  a  ray  or  beam  of 
light  on  passing  from  an  optically  rarer  medium  to  an 
optically  denser  one  is  bent  towards  the  normal  at 
the  point  of  impact,  so  a  beam  of  sound  in  passing 
from  a  lighter  gas  to  a  denser  one  is  bent  in  the 
same  way.  If  it  passes  into  a  lighter  gas,  it  is 
bent  away  from  the  nor-  FJG 

mal.  It  is  possible  to  con- 
struct gas  sound  lenses 
on  this  principle.  Let  a 
whistle,  w  (fig.  43),  be  at 
such  a  distance  from  the 
singing  flame,  sf,  as  just 
to  affect  it.  Fill  a  toy  caoutchouc  balloon  with 
G 


82  Practical  Physics. 

air,  and  hold  it  close  to  the  flame ;  the  flame  still 
flares.  Fill  a  similar  balloon  with  hydrogen,  and 
place  it  in  the  same  position;  the  flame  ceases  to 
flare,  because  the  balloon  acts  then  as  a  dispersing  lens. 
Remove  the  balloon,  and  reduce  the  gas  so  that  the 
flame  ceases  to  flare,  then  introduce  a  similar  balloon 
in  the  same  place  filled  with  carbonic  acid ;  the  flame 
now  flares,  because  the  balloon  acts  as  a  condensing 
lens. 

It  is  well  known  that  sound  travels  with  less  loss 
through  air  of  uniform  density  than  through  a  hetero- 
geneous atmosphere.  This  appears  to  be  the  reason 
why  sounds  are  heard  distinctly  in  frosty  weather, 
where  by  contact  with  snow  or  ice-cold  ground  the  air 
is  of  a  pretty  uniform  temperature,  and  contains  the 
same  amount  throughout  of  aqueous  vapour.  Also 
when  the  air  is  throughout  of  the  same  temperature 
and  saturated  with  moisture,  as  after  a  shower  of  rain, 
sounds  are  distinct.  The  obstruction  of  mist  particles 
to  sound  is  not  so  hostile  to  its  clearness  as  variation 
Flf%  44  in  density.  This  is  shown 

experimentally  by  placing 
W  the  sensitive  flame  at  one 
end   (fig.   44),    and    the 
whistle  at  the  other  end 


r 


fllj11""  "of  a  long  box  open  at 
both  ends,  and  arranging  the  flame  so  as  just  to  flare. 
Then  if  carbonic  acid,  or  steam,  or  coal  gas  be  allowed 
to  enter  through  several  jets  in  the  bottom  of  the  box, 
the  flame  ceases  to  flare!  If  coal  gas  is  employed, 
the  box  should  be  tilted  a  little  upwards  towards  the 
whistle,  to  prevent  an  explosion. 


Transverse  Vibrations  of  Rods.          83 


ORIGINS   OF   SOUND  WAVES. 

§  84.     Transverse    vibrations    of  rods.  —  If  a 

square  rod  is  fastened  rigidly  at  one  end,  and  plucked 
at  the  other  end,  it  will  swing  backwards  and  forwards 
at  a  certain  rate,  and  if  it  be  not  plucked  too  far,  its 
rate  of  swinging  is  the  same,  whether  its  excursion  be 
great  or  small.  The  rate  of  swinging,  that  is,  the 
number  of  swings  to  and  fro,  depends  upon  the  elas- 
ticity of  the  rod,  upon  its  density,  and  also  upon  its 
length  and  thickness  in  the  direction  of  swing.  If 
we  are  considering  rods  of  the  same  material,  and 
examining  them  at  the  same  time,  density  and  elasti- 
city are  out  of  count,  because  they  are  constant.  It 
is  found  that  if  n  be  the  number  of  vibrations  to  and 
fro  in  a  given  time,  /  be  the  length  of  the  rod,  and  / 
its  thickness  in  the  plane  of  vibration, 


To  prove  this,  take  a  carefully  planed  deal  rect- 
angular rod,  i  in.  wide,  \  in.  thick  exactly,  and  about 
12  ft.  long.  Clamp  it  firmly  between  cardboard  in  a 
vice  horizontally,  and  so  that  its  \  in.  faces  are  hori- 
zontal, and  so  that  10  feet  are  free.  Set  it  swinging 
gently  horizontally.  It  will  hang  down  in  a  curve, 
but  this  does  not  matter.  Adjust  a  leaden  bullet  at 
the  end  of  a  silk  thread,  so  as  to  swing  at  the  same 
rate  as  the  rod.  Adjust  another  such  pendulum  to 
swing  twice  as  fast  as  the  first.  Now  shorten  the  rod 
till  it  swings  at  the  same  rate  as  the  second  pendulum  : 
on  measuring  the  rod  it  is  found  to  be  about  7  ft.  long. 
G  2 


84  Practical  Physics. 

»«  =  2«1,    ^2=2^2,    -^2=2— 2  nearly. 

This  shows  that  the  number  of  oscillations  varies  in- 
versely with  the  square  of  the  length.  Now  return  to 
the  10  ft.  length,  but  turn  the  rod,  so  that  the  i  in. 
faces  are  horizontal.  It  will  now  be  found  to  swing 
with  the  shorter  pendulum,  that  is,  twice  as  fast  as  it 
did  when,  being  of  the  same  length,  it  was  of  double 
thickness  in  the  direction  of  swing.  Accordingly,  if 
we  take  a  nicely- worked  square  steel  rod,  and  clamp 
it  at  one  end  rigidly,  and  furnish  the  top  with  a  bright 
bead,  so  that,  by  the  retention  of  images,  the  reflection 
of  a  flame  in  the  bead  appears  as  a  streak  of  light,  we 
FIG.  45.  shall  get  a  line  of 

light  (i)  if  the  rod 
is  plucked  from  a 
to  ft,  also  a  line 
I  \  /  f^\  r\  /;  (2)  if  it  is  plucked 
I  \  /  V_y  \J  C/  from  c  to  d;  it  will 
*  2  3  *  6  6  7  trace  out  the  line 
(3)  if  plucked  simultaneously  from  a  to  b,  and  from 
d  to  c ;  the  line  (4)  will  be  shown  if  it  be  plucked 
simultaneously  from  b  to  a  and  d  to  c.  If  in  case  (2) 
when  the  point  has  performed  a  quarter  of  its  path,  the 
rod  receives  an  equal  blow  from  a  to  £,  it  will  travel  in  a 
circle  (5).  If  it  receive  such  a  blow  when  it  has  nearly 
completed  its  (2)  motion,  it  will  trace  out  the  ellipse 
(6).  If  it  receive  the  blow  soon  after  starting,  it  will 
describe  the  ellipse  (7).  In  the  cases  (3),  (4),  (5),  (6), 
(7),  where  both  motions  are  imparted,  it  is  seen  that  a 
point  moving  along  the  curve,  or  up  and  down  the  line, 
moves  as  often  up  and  down  as  to  the  right  and  left. 


Transverse  Vibrations  of  Rods.          8$ 

If  (fig.  46)  the  rod  be  twice  as  thick  one  way  as 
the  other,  and  it  receive  simultaneous  impulses  from 
d  to  c  and  from  b  to 
0,  it  will  swing  to  the 
left  and  back  again 
while  it  is  moving  up 
(in  the  figure),  and 
to  the  left  and  back 
while  it  is  moving 
down,  and  so  trace  *•'  *  3  &  $ 

out  (i).  If  it  receives  simultaneously  an  impulse 
from  d  to  c  and  an  impulse  from  a  to  b,  it  will,  for 
similar  reasons,  trace  out  the  curve  (2).  If,  when,  by 
reason  of  the  impulse  from  d  to  c,  it  has  got  half  up, 
it  receives  an  impulse  from  a  to  b,  it  will  describe  the 
figure  of  8,  (3) :  (4),  and  (5)  show  the  curves  traced 
out,  when  the  a  b  impulse  is  imparted  at  different 
phases  of  the  cd  motion.  In  all  cases,  a  point  passing 
along  these  curves  travels  twice  as  often  to  the  right 
and  left  as  up  and  down. 

If  the  width  of  the  rod  be  to  the  breadth  as  2  to  3, 
figures  must  be  formed  of  such  a  kind  that  a  point 
moving  over  them  passes  three  times  pIG.  47. 

from  left  to  right  and  back  while  it 
passes  twice  up  and  down.  These 
conditions  will  be  seen  to  be  ful- 
filled by  figures  of  which  types  are 
shown  in  fig.  47. 

Other  ratios,  such  as  3  :  4,  3  :  5, 
4:5,  &c.,  give  characteristic  figures  of  more  complex 
shape.  As  the  vibrations  die  out  the  point  of  the 
rod  makes  shorter  and  shorter  excursions  in  both 
directions.  So  that,  for  instance,  in  the  first  case,  with 


86  Practical  Physics. 

the  square  rod  the  lines  (3)  and  (4)  become  shorter, 
(5)  becomes  a  circular  spiral,  and  (6)  and  (7)  become 
elliptic  spirals  preserving  their  eccentricity  and  the 
directions  of  their  axes.  But  if  a  b  be  a  little  longer 
than  c  d  the  point  will,  starting  from  case  (3),  have 
come  a  little  back  to  the  right  before  it  begins  to  move 
down,  and  it  will  have  got  twice  as  much  to  the  right 
before  it  begins  to  move  up,  and  so  on.  It  will  form 
a  curve  which  apart  from  its  fading  off  is  not  a  closed 
curve,  but  which,  as  only  a  fraction  of  it  is  visible  at 
once,  changes  in  aspect  from  (3)  to  (6),  from  (6)  to 
FIG.  48.  (5),  from  (5)  to  (7),  from  (7)  to  (4),  from 
(4)  to  (7),  to  (5),  to  (6),  to  (3).  So  when 
the  dimensions  are  as  2  :  i  (fig.  46),  if 
there  be  a  little  defect  in  the  ratio,  the 
figure  will  pass  from  (i)  to  (4),  to  (3),  to 
(5),  to  (2),  to  (5),  to  (3),  to  (4),  to  (i). 
And  so  for  other  cases.  If  both  defect 
in  ratio  and  fading  off  occurs,  a  spiral  is 
traced,  out  of  which  an  idea  is  given  in  fig.  48. 

§  85.  These  figures  can  be  imitated  artificially,  and 
the  whole  course  of  the  point  registered  graphically,  by 
FIG.  49.  pivoting  two  pendulums  to 

two  adjacent  sides  of  a  square 
table,  and  fastening  with  some 
vulcanised  caoutchouc  joints 
two  arms  to  the  upper  parts 
of  the  pendulums  at  right 
angles  to  one  another  in  a 
horizontal  plane.  The  ends 
of  the  arms  are  also  joined 
together  by  a  ball  and  socket  joint  or  by  a  Hooke's 


Composition  of  Vibrations. 


joint  This  joint  carries  a  vertical  glass  tube  pen 
charged  with  aniline  colour,  or  a  style  to  scratch 
lampblack  off  smoked  glass. 

Use  is  made  of  the  constancy  of  these  figures  or 
the  reverse  to  test  the  consonance  of  tuning-forks, 
and  to  make  one  fork  either  be  in  perfect  unison  with 
another,  or  at  a  known  interval  from  it.  Thus  to  adjust 
a  fork  to  be  in  uni-  FIG.  50. 

son  with  the  fork  N, 
a  beam  of  light,  L 
(fig.  50),  is  thrown 
upon  the  polished 
face  of  one  prong  of 
N  which  is  vertical, 
thence  it  is  reflected 
and  strikes  the  po- 
lished face  of  one 
prong  of  A,  thence 
it  is  reflected  and 
falls  upon  a  screen  at  /.  If,  however,  the  prongs  of 
N  are  bent  in,  as  the  dotted  lines  represent,  the  light 
strikes  with  a  greater  incident  angle  at  a',  is  reflected 
higher  on  the  prong  of  A,  and  reaches  the  screen  at  /'; 
when  the  prong  of  N  is  bent  outwards  the  light  will 
be  reflected  to  /15  so  that  as  the  prong  moves  in  and 
out  the  spot  of  light  travels  rapidly  from  /'  to  /x  and 
back,  forming  a  vertical  streak.  If  A  be  bowed  at  the 
same  time  and  its  prongs  are  bent  inwards  at  the 
same  time  as  those  of  A,  the  light  reflected  from  a 
will  strike  the  fork  A  at  b'  with  greater  incidence  than 
before,  and  the  ray  will  be  reflected  to  /' .  When  the 
prongs  of  both  forks  are  bent  outwards  the  light  will 


88  Practical  Physics. 

appear  at  /2,  so  that  when  both  forks  are  sounding, 
a  streak  of  light  extends  from  /"  to  /2.  Suppose  now 
the  fork  A  to  be  a  little  out  of  tune,  and  to  be  a  little 
too  high  or  swift  in  its  vibration,  the  reflecting  prong 
of  A  will  have  come  a  little  back  when  the  prong  of  N 
has  reached  the  end  of  its  excursion,  so  that  the  light 
will  fall  a  little  lower  than  /'.  When  the  N  prong 
is  bent  outwards,  the  A  prong  will  be  twice  as 
much  in  advance,  and  the  spot  will  be  twice  as  far 
above  /2  as  it  was  below  I",  and  so  on,  until 
the  A  prong  is  upright,  when  N  is  at  its  maximum 
excursion,  that  is,  J  of  a  complete  vibration  to  and/w, 
in  advance  of  N.  The  streak  of  light  will  then  reach 
from  /'  to  /!.  In  double  the  time  A  will  be  half  a 
vibration  in  advance  of  N,  that  is,  when  the  prong 
of  N  is  bent  in  to  its  utmost,  the  prong  of  A  is  benc 
out,  the  last  bends  the  ray  down  as  much  as  the  first 
bends  it  up,  so  that  there  is  only  a  spot  of  light  at  /. 
This  begins  immediately  to  grow  until  A  is  a  complete 
vibration  in  advance  of  N.  The  forks  are  now  again  in 
the  same  phase,  and  the  maximum  length  of  streak  is 
obtained.  To  bow  a  fork  without  stopping  it  or 
altering  its  phase,  the  bow  is  made  to  touch  the  fork 
with  a  sliding  motion.  The  shortening  and  lengthen- 
ing of  the  line  of  light  (which  is  easily  distinguished 
from  the  shortening  due  to  languishing,  for  the  latter 
is  not  followed  by  lengthening)  takes  place  the  more 
quickly  the  greater  the  disagreement  between  the 
forks.  To  see  whether  the  fork  A  is  too  fast  or  too 
slow,  for  the  effect  on  the  light  line  would  be  the 
same,  one  prong  of  A  is  loaded  with  a  little  wax  con- 
taining a  swan  shot.  If  this  makes  the  gaping  of  the 


Transverse   Vibrations  of  Rods.          89 

line  more  rapid  of  course  the  fork  was  already  too 
slow,  for  loading  diminishes  the  rate.  If  loading 
makes  the  gaping  of  the  line  less  rapid,  the  fork  A  is 
too  quick  ;  in  the  former  case  metal  is  filed  off  the 
upper  part  of  the  prongs,  for  this  unloads  them  without 
diminishing  the  elasticity.  In  the  latter  case  metal  is 
filed  off  the  root  of  the  fork,  for  this  diminishes  the 
elasticity  without  sensibly  affecting  the  inertia. 

For  other  ratios  besides  I :  I,  as  when  we  wish  to 
adjust  a  fork  so  as  to  be  the  higher  octave  of  the  fork 
N,  one  fork,  say  N,  is  clamped  vertically  as  before,  and 
this  alone  would  give  a  vertical  streak.  The  fork  to 
be  adjusted  is  clamped  horizontally  with  its  polished 
face  vertical.  This  alone  would  give  a  horizontal 
streak.  When  the  two  forks  are  sounded  together,  if 
their  rates  are  nearly  in  the  ratio  of  i  :  2,  a  curve  of 
light  resembling  one  of  those  in  §  84  will  be  formed, 
and  this  will  pass  more  or  less  rapidly  through  the 
figures  (i)  (4)  (3)  (5)  (2)  according  as  the  octave- 
harmony  is  less  or  more  perfect.  As  before,  loading 
the  fork  shows  whether  it  is  too  fast  or  too  slow,  and 
it  has  to  be  filed  as  before  till  one  of  these  forms 
remains  constant  for  a  long  time.  If  it  takes  a  minute 
for  the  figures  to  pass  through  all  shapes  and  return  to 
its  original  shape,  this  means  of  course  that  the  fork  A 
in  a  minute  gives  one  vibration  more,  or  one  vibration 
less  than  twice  the  number  made  by  N  in  a  minute. 
So  that  if  N  gives  520  complete  vibrations  in  a  second 
or  31,200  in  a  minute,  A  gives  62,399  in  a  minute  or 
1039-983  in  a  second  instead  of  1040-  which  is  the 
higher  octave  of  N.  This  to  the  ear  would  be  perfect 
harmony. 


92  Practical  Physics. 

reflected  from  the  fixed  end,  returns  reversed  and 
bursts  into  the  empty  tube  with  increased  velocity  and 
amplitude. 

If  we  take  one  of  the  above  tubes  and  by  a  motion 
of  the  hand  send  a  series  of  complete  waves  down  it 
of  such  a  length  that,  when  the  front  of  the  reflected 
first  elevation  (in  the  form  of  a  depression)  has 
reached  the  middle,  the  front  of  the  second  elevation 
FIG.  51.  reaches  the  middle  coming  in  the 

" opposite  direction,  the  middle  point 
will  be  pushed  up  and  down  at  the 
same  time  with  the  same  pressure 
and  will  remain  at  rest.  When  this 
second  elevation  has  reached  the 
end  the  reflected  first  elevation  has 
reached  the  beginning.  It  is  seen 
that  each  contour  of  the  cord,  i,  2,  3,  is  a  complete 
wave,  so  that  the  wave-length  is  equal  to  the  length  of 
the  cord.  Now  the  point  m  being  always  at  rest 
because  it  is  always  subjected  to  equal  and  opposite 
pressures  may  be  considered  rigid.  That  is,  instead  of 
one  cord  vibrating  in  two  segments  with  a  node 
between,  one  segment  moving  up  as  the  other  moves 
down,  we  may  consider  each  half  by  itself  moving  up 
FIG.  52.  and  down  between  two  fixed 

^ ^  points.     It  will  keep  the  same 

time  as  the  two  together.  The 
length  of  the  cord  is  now  only  half  the  wave- 
length. 

Now  (comp.  §  77)  the 

number  of  vibrations  =  — ve  °C1  ^    . 
wave-length. 


Stationary   Waves.    Nodes.  93 

and  since 


it  follows  that  if  /  be  the  length  of  the  cord 


m 

Though  thus  derived  from  the  advance  and  reflexion 
of  two  elevations  or  depressions,  we  may  pluck  the 
middles  of  the  two  halves,  the  one  up  and  the  other 
down,  simultaneously  and  observe  the  segmental 
vibration  with  the  central  node.  So  when  the  cord 
vibrates  as  a  whole,  being  plucked  in  the  middle,  we 
may,  if  we  choose,  regard  its  two  halves  as  being  re- 
flected from  the  two  fixed  ends.  Although  above  (p  90) 
we  neglected  the  automatic  depression  which  accom- 
panied the  elevation,  when  the  end  is  rigidly  fastened 
this  depression  or  reflexion  from  the  beginning  is  of 
absolute  importance.  Thus  when  a  wire  is  struck  at 
a  quarter  its  length  from  one  fixed 
end,  its  successive  conditions  are 
shown  in  fig.  53.  That  is,  while  part 
of  the  stored  energy  of  the  displaced 
segment  determines  the  progression 
of  the  depression  to  a',  the  other 
part  carries  the  segment  back  across 
the  normal  line  producing  an  ele- 
vation. 

§  87.  With  the  elastic  tube  one  can  study  the 
growth  and  establishment  of  such  segmental  vibra- 
tions or  stationary  waves.  Taking  one  of  the  elastic 


94  Practical  Physics. 

tubes  move  the  hand  quickly  to  and  fro  and  by  and 
bye  the  cord  and  the  hand  will  fall  into  one  another's 
FIG.  54.  humour  and  the  cord  will  fall  into 

segments  separated  by  nodes. 

The  rate  of  vibration  of  the 
segments  is  inversely  proportional 
to  their  lengths,  that  is  proportional 
to  their  number.  That  such  seg- 
mentary  vibration  when  once  estab- 
lished is  automatic  is  shown  by 
rigidly  fixing  an  elastic  tube  in  a 
vertical  position  and  while  gently 
restraining  (damping)  the  middle  by  letting  it  pass 
between  the  fingers,  plucking  the  middle  of  one-half. 
The  tube  being  released  vibrates  in  two  segments  with 
a  central  node.  Damped  at  one-third  and  plucked  at 
one  sixth  from  the  bottom  it  vibrates  in  three  seg- 
ments and  so  on.  In  this  experiment  it  should  be 
remembered  that  the  upper  part  of  the  tube  has  a 
little  the  greater  tension,  so  that  the  upper  segment  to 
be  synchronous  with  the  lower  segment  should  be  a 
little  the  longer  :  and  so  for  the  other  cases. 

FIG.  55-  §  88.  By  the  elastic  cord  it  can 

be  shown  that  a  string  may  vibrate 
as  a  whole  and  in  segments  at  the 
same  time  provided  there  is  always 
either  an  odd  or  an  even  number 
of  automatic  nodes  :  and  in  all 
cases  however  it  may  be  vibrating 
in  segments  it  can  vibrate  as  a 
whole. 
The  nodes  on  wires  are  well  shown  by  stretching 


Sounds  of  Vibrating  Strings.  95 

a  wire  several  feet  long  horizontally  and  dividing  it 
into  eight  equal  parts  by  seven  stirrups  of  paper 
resting  on  the  wire.  The  second  stirrup  from  one 
end  is  gently  pinched  around  the  wire  and  the  wire  is 
gently  plucked  where  the  first  stirrup  rests.  The  $rd, 
5th,  and  yth  stirrups  will  be  jerked  off,  for  they  are  at 
the  centres  of  segments  ;  the  4th,  5th,  and  6th  will 
retain  their  places,  for  they  are  at  nodes. 

§  89.  Vibrating  strings  as  sources  of  sound.—  The 
conditions  which  determine  the  rate  of  vibration  of  a 
stretched  string  or  wire  are,  as  we  have  seen,  the 
stretching  pressure  or  weight  hung  at  one  end,  the 
length  and  the  mass 


or  in  an  unloaded  string  since  m  a  d*  if  d  be  the 
diameter,  for  the  same  material 


Steel  wires  (pianoforte  wires)  are  the  most  convenient 
for   studying   this 

....  .  r  10.56. 

relationship.        A 

table  (fig.  56)  has 

two     iron      pegs 

driven     obliquely 

in    at    one     end. 

At  the  other  end 

are  two  pulleys  let  into  the  table  so  that  their  axes 

are  on  the  table.     Two  mahogany  wedges  nearly  of 

the  same  height  as  the  pulleys,  are  permanently  fixed 

at  the  same  distance  from  the  pulleys,  so  that  measured 


96  Practical  Physics. 

from  the  top  of  the  wedge  to  the  top  of  the  pulley 
there  is  a  whole  number  of  units  of  length,  say  64  in. 
Two  other  movable  wedges  or  bridges  a  little  higher 
than  the  fixed  ones  are  provided,  and  the  table  is 
divided  into  inches  numbered  from  the  axes  of  the 
pulleys.  The  wires  being  horizontal  the  vibrating 
length  is  the  distance  from  the  top  of  the  pulley  to  the 
top  of  the  bridge,  or  from  the  axis  of  the  pulley  to  the 
centre  of  the  base  of  the  bridge.  Let  wires  of  the 
same  metal  and  the  same  gauge  be  fastened  to  the 
pegs  and  passed  over  the  pulleys.  Bring  the  movable 
bridges  to  any  the  same  distance  from  the  pulleys,  say 
1 8  in.,  and  hang  a  weight  of  say  10  Ibs.  at  the  end  of  one 
wire,  and  also  10  Ibs.  at  the  end  of  the  other.  The  two 
wires  are  perfectly  identical  and  under  identical  con- 
ditions :  plucked  gently  and  in  the  middle  they  will  give 
identical  notes.  Weight  now  one  of  the  wires,  further. 
Its  note  will  rise  in  pitch  till  it  is  weighted  with  40  Ibs., 
whereupon  it  will  give  out  the  easily  recognisable 
higher  octave  of  the  other  wire.  And  so,  whatever  be 
the  weight  or  stretching  pressure  on  the  first  wire,  and 
whatever  its  length,  the  second  will  give  the  higher 
octave  of  the  first,  provided  its  length  is  the  same, 
when  the  weight  on  the  second  is  4  times  as  great  as 
that  on  the  first  With  short  wires,  say  i  foot  long,  this 
can  be  repeated.  For  suppose  both  wires  are  stretched 
with  5  Ibs.,  then  one  with  20,  then  the  first  being 
stretched  by  80  Ibs.  will  give  the  higher  octave  of  the 
second,  or  the  second  octave  above  its  original  note, 
that  is  4  times  its  original  number  of  vibrations. 

Birmingham  steel  wire  of  14  gauge  will  easily  bear 
a  strain  of  n  2  Ibs.  if  there  are  no  kinks  in  it.     Such 


Vibrating  Strings.  97 

experiments,  and  they  can  be  multiplied  without 
limit,  prove  that  n  oc  Vs. 

Start  with  the  wires  of  equal  length,  stretched  with 
10  and  40  Ibs.  respectively,  then  move  the  bridge 
of  the  first  wire  till  the  length  of  that  wire  is  halved. 
The  notes  will  now  be  in  unison,  showing  that  halving 
the  length,  other  things  jemaining  unchanged,  has' 
doubled  the  number  of  vibrations.  Or  start  with 
two  wires  of  the  same  length,  stretched  with  5  and 
80  Ibs.  respectively,  so  that  the  second  gives  four 
times  as  many  vibrations  as  the  first  and  move  the 
bridge  of  the  5  Ib.  wire  till  its  length  is  only  one 
quarter  of  that  of  the  80  Ib.  wire,  unison  is  restored. 

These   experiments  prove  that  n  a  j.     Both  these 

relationships  can  be  elegantly  verified  in  the  following 
manner.  Put  the  bridge  of  the  one  wire  at  any  whole 
number  of  inches,  say  30,  and  fasten-to  the  wire  a 
known  weight,  say  56  Ibs.  Hang  from  the  other  wire 
an  unknown  weight  in  a  bag.  Move  the  bridge  of  the 
second  wire  till  there  is  unison.  Suppose  this  distance 
be  found  to  be  24  inches.  Then,  since  there  is 
unison,  if  x  be  the  unknown  weight — 

^56"^  ^Z or  -5!  =  _* _  or  x  =  35.86  lbs. 
30        24         900        576 

On  actually  weighing  the  bag  of  weights  the  result 
agrees  generally  within  one  or  two  ounces. 

To  confirm  the  relationship  n  oc  L,  it  is  necessary 

to  determine  d  with  great  accuracy,  or  rather  to 
compare  accurately  the  diameter  of  one  wire  with  that 

H 


98  Practical  Physics. 

of  the  other.  This  is  best  done  by  measuring  exactly 
equal  lengths  of  the  two  wires  and  weighing  them,  the 

weights  being  w^  and  w2,  then  -L  =  ^_^i  .     Let  two 

^2        VWz 

such  wires  be  of  equal  length,  vary  the  stretching 
pressure  on  one  till  there  is  unison.  It  is  then  found 
that  the  square  roots  of  the  stretching  pressures  are 
directly  as  the  diameters,  or  the  stretching  pressures 
are  directly  as  the  weights  of  the  wires  — 


V  ^ 

Or,  taking  equal  stretching  pressures,  vary  the  lengths 
till  there  is  unison,  it  is  then  found  that  the  lengths 

are  inversely  as  the  thicknesses  -L  =  _2,  or  the  square 

/2       #! 

/  2       w 
of  the  lengths  inversely  as  the  weights  ~  =  —  • 

The  relative  diameters  of  dissimilar  metals  are  ob- 
tained by  weighing  equal  lengths,  taking  the  square 
roots  of  the  weights,  and  dividing  by  the  specific 
gravities. 

§  90.  Musical  scale.  —  The  scale  most  generally 
in  use  is  formed  as-fcllows.  Let  a  note  consist  of  n 
vibrations  a  second.  Then  — 

Note  Major  Major        Major 

Tonic      Second      Third       Fourth       Fifth      Sixth       Seventh        Octave 

n         |«        |#        ^n        |#      f«        y/z         2n. 

Sometimes  the  'middle  C'  is  taken  as  having  256 
vibrations  a  second  ;  the  eight  complete  notes  from 
this  C  to  its  higher  octave  are  — 


Musical  Scale.  99 

CDE'F         G         A          B        c 
256     288     320    341-3     384    426-6    480    512. 

Whole  numbers  are  obtained  throughout  if,  as  is 
sometimes  done,  264  vibrations  are  given  to  C — 

CD  EF  GA  B  C 

264     297     330     352     396     440    495     528. 

Suppose  therefore  we  have  a  wire  stretched  over  a 
board  between  two  pegs,  one  of  which  is  fixed  and 
the  other  has  a  hole  in  it  through  which  the  wire 
passes,  and  suppose  we  have  a  bridge  at  a  distance  / 
from  the  peg  with  the  hole.  The  latter  can  be  turned 
round  with  a  key  if  it  has  a  square  head  until  the 
length  /  is  in  unison  with  a  C  luning-fork.  Divide  the 
distance  /  into  lengths,  namely — 

CDEFGA  B  C 

I     ¥     ¥      ¥     ¥     V     */     V- 

Then  the  bridge  being  placed  at  one  or  other  of  these 
places,  the  wire  will  give  the  corresponding  note.  Such 
a  wire  with  its  scale  is  a  monochord. 

In  the  harp,  pianoforte,  and  other  stringed  instru- 
ments, the  number  of  vibrations  per  second  which 
each  string  gives  is  determined  partly  by  the  string's 
length,  partly  by  its  weight,  and  partly  by  its  tension. 
That  is,  the  strings  producing  the  higher  notes  are 
not  only  the  shortest ;  they  are  the  thinnest  and  are 
stretched  the  most.  The  wires  of  the  graver  notes  are 
loaded  with  spirals  of  thin  wire.  To  avoid  '  thinness' 
of  sound,  which  accompanies  thin,  i>hort,  highly 
strung  wires,  several,  two  or  three,  similar  wires  are 
placed  side  by  side  and  struck  by  the  same  hammer. 

H2 


ioo  Practical  Physics. 

This  enriches  the  note.  The  c  tuning'  is  always 
effected  by  varying  the  tension,  that  is,  turning  one  of 
the  pegs  to  which  the  wire  is  fastened.  The  hammer 
is  not  applied  at  the  centre  of  the  wire  so  as  to  sound 
only  the  fundamental  note,  but  at  such  a  distance 
from  the  end  that  besides  the  fundamental  note  har- 
monics are  sounded  as  well,  which  enrich  the  sound, 
without,  to  most  ears,  impairing  its  purity. 

§  91.  Further  development  of  nodes, — Nodes  in 
rods. — In  §  84  we  considered  the  note  of  a  rod 
vibrating  as  a  whole,  and  found  that  the  rate  of  vibra- 

on  varied  inversely  with  the  square  of  the  length. 
FIG.  57.  A  longish  rod  or  wand    may  be 

,    ^-----^^^^^    easily  shaken  at  one  end  so  as  to 
"  divide  itself  into  two  parts,  a  seg- 

^z^^js*^*****"  nient  and  half  a  segment,  separated 
===:3  by  a  node  rather  less  than  one-third 
from  the  free  end.  By  a  more  rapid  motion  two 
segments  and  a  half  may  be  got,  there  being  then  two 
automatic  nodes,  one  at  nearly  one-fifth  and  the  other 
at  nearly  three-fifths  from  the  free  end.  As  the  seg- 
ment and  the  free  part  vibrate  at  the  same  rate,  the 
rate  of  vibration  of  the  whole  may  be  very  roughly 
considered  as  the  rate  of  the  half  segment  at 
the  end,  that  is  the  rate  of  a  rod  of  length  ^/ 
fastened  at  one  end.  Since  the  number  of  vibrations 
varies  inversely  with  the  square  of  the  length,  the 
number  of  vibrations  of  the  Fundamental  note  beings, 
the  number  now  is  9  x  //,  and  if  there  are  two  nodes  it 
is  25  xn  and  so  on.  These  are  the  first  and  second 
harmonics.  The  nodal  line  can  be  traced  on  a  tuning- 
fork  when  it  is  sounding  its  first  harmonic  by  holding 


Nodes  of  Rods.    Bells.  101 

it  horizontally  with  the  broad  face  of  the  prongs  hori- 
zontal, scattering  sand  on  both  prongs  and  bowing 
near  the  root  of  the  fork.  All  the  sand  except  that 
which  is  over  the  nodal  line  is  thrown  off. 

If  we  hold  an  elastic  rod  in  the  middle  and  move 
the  middle  transversely  to  and  fro,  the  rod  will  fall 
into  one  whole  and  two  half  seg-  FJG  ^ 
ments,  separated  by  two  automatic  ^>c^~~^><^"" 
nodes ;  the  rate  of  vibration  in  this 
case  must  be  16  times  as  fast  as  that  of  the  fundamen- 
tal note.  The  nodes  are  at  £  the  length  of  the  rod 
from  its  ends.  A  strip  of  glass  laid  on  two  parallel 
threads  at  the  distance  of  the  nodes  apart  and  lightly 
fastened  to  the  threads  gives  off  a  highly  clear  note 
when  struck  in  the  middle.  It  is  the  note  of  the 
*  musical  glasses.'  In  order  to  get  the  gamut  of  the 
musical  glasses,  if  the  lengthjpf  the  first  glass  is  /1?  that 
of  the  second  must  be  /j  >/|,  that  of  the  third  /t  V^9 
and  so  on  (comp.  §  yo).  Strips  of  glass  of  these  lengths 
being  cut,  they  are  supported  at  a  quarter  their  lengths 
from  their  ends  on  stringsand  form  a  scale  of  whole  notes 

§  92.  The  Bell. — If  we  hold  a  circular  elastic 
hoop  on  two  opposite  sides  and  bend  it  F 
in  and  out  rapidly,  we  find  that  at  four 
points  there  are  nodes,  and  between  them 
segments  (quadrants)  which  move  in  and 
out,  the  points  of  maximum  motion  being 
four  in  number  and  situated  midway 
between  the  nodes.  Such  is  the  motion  of  a  bell 
when  sounding  its  fundamental  note.  This  is  shown 
by  employing  an  inverted  bell  or  goblet  and  bowing 
it.  If  while  it  is  sounding  a  little  pellet  of  wax  hung 


IO2  Practical  Physics. 

from  a  thread  is  carried  round  the  edge  outside  so  as 
always  to  lean  upon  the  goblet,  it  is  thrown  off  with 
violence  where  the  goblet  was  bowed,  and  also  at 
the  opposite  region,  and  also  at  quarter  circumference 
distance  from  these  points.  But  at  the  intermediate 
points,  £  circumference  distance  from  these,  the  pellet 
remains  comparatively  at  rest.  If  the  goblet  be  filled 
with  water  and  then  bowed  as  before,  the  water  is 
thrown  into  great  commotion  at  the  bowing  place  and 
quadrant  distances  from  it,  but  at  the  nodes  it  remains 
more  tranquil. 

The  note  given  out  by  a  drum  depending  upon 
the  vibration  of  a  membrane  is  seldom  pure  ;  the 
membrane  breaks  up  into  independently  vibrating 
pieces  according  to  the  place  where  it  is  struck.  The 
clash  and  clang  of  cymbals  and  the  rattling  boom  of 
a  gong  are  characteristic  of  the  variety  of  air  waves 
FIG.  60.  to  which  they  give  rise. 

-^  j>  /The  clap,  rattle,  roll  and 

(       \  '  >       /    boom  of  thunder  denote 

ci^          J&taei   i&u>    Zoom,  the  course  of  the  light- 
ning flash  and  its  attitude  towards  us. 

§  93.  Nodes  and  segments  in  vibrating  plates. — 
If  a  uniform  circular  brass  plate  about  i  foot  in  diameter 
be  clamped  by  a  screw  in  the  middle,  it  can  be  made 
to  break  up  into  any  even  number  of  sectors  greater 
than  two  and  maintain  its  own  vibration,  giving  out 
notes  of  higher  pitch  according  as  the  number  of 
sectois  is  greater.  These  sectors  so  pulsate  that 
when  one  is  moving  in  one  direction  the  two  neigh- 
bouring ones  are  moving  in  the  opposite.  The  sec- 
tors are  separated  by  radial  nodal  lines  upon  which 


Vibrations  of  Plates.  103 

strewn  sand  accumulates  when  the  plate  is  sounded, 
thus  tracing  out  the  posi- 
tion of  the  nodes. 

The  formation  of  these 
lines  is  assisted  by  gently 
pressing  the  plate  with  a 
point  where  the  node  should  meet  the  circumference. 
Thus  in  (i)  the  plate  is  bowed  at  b  and  the  finger/* 
touches  the  plate  at  ^th  of  the  circumference  from  b. 
The  plate  gives  out  its  lowest  or  fundamental  note. 
In  (2)  the  finger  is  placed  at  T^th  the  circumference 
from  l>,  in  (3)  at  y^th,  in  (4)  at  ^th,  and  so  on.  At 
the  beginning  of  the  stroke  the  bow  should  be  pressed 
firmly  and  moved  slowly  across  the  edge  at  an  angle 
of  about  80°.  As  soon  as  the  plate  begins  to  speak 
a  lighter  and  more  rapid  stroke  is  given. 

§  94.  If  a  round  glass  plate  be  clamped  at  a  dis- 
tance of  £rd  its  radius  from  its  edge,  and  a  bundle  of 
well  resined  horsehairs  be  drawn  with  lateral  pressure 
through  a  small  hole  in  the  middle  (fig.  62)  FlG 
the  sand  collects  in  a  ring  at  one-third  the 
radius  from  the  edge.  The  vibration  of  a 
round  plate  and  the  vibration  of  a  rectan- 
gular plate  in  §  91  are  the  counterparts  of 
the  water  mononodal  undulation  in  a  cylindrical 
trough  and  the  binodal  undulation  in  a  rectangular 
trough  (§§  77,  78). 

§  95.  With  a  square  plate  clamped  in  the  middle 
an  almost  endless  variety  of  segmental  vibrations  and 
corresponding  sand-marked  nodal  lines  can  be  formed. 
It  will  be  noticed,  and  is  indeed  an  essential  condition 
of  all  free  vibration,  that  the  number  of  vibrating 


104 


Practical  Physics. 


elements  is  even,  and  that  all  symmetrically  situated 
elements  are,  at  the  same  time,  in  the  same  phase  of 
motion. 

FIG.  63. 


/     b 

These  figures  can  be  rendered  permanent  by  un- 
screwing the  nut  which  secures  the  plate  in  the 
middle,  and  pressing  upon  the  sand  figure  some 
gummed  cardboard. 

§  96.  The  Gas-wave. — That  continuity  of  matter 
is  essential  for  the  production  of  sound  is  shown  by 
setting  a  hammer  to  strike  a  bell  under  the  exhausted 
receiver  of  an  air-pump.  If  the  hammer  and  bell  be 
hung  or  supported  by  non-resonant  matter,  the 
vibrations  of  the  bell  are  almost  inaudible.  If,  instead 
of  air,  hydrogen  be  admitted  into  the  vacuum,  the 
vibrations  continue  to  be  almost  inaudible.  For  even 
when  the  tension  inside  the  receiver  is  restored,  the 
blow  which  the  lighter  gas  (which  is  only  ^  as  dense 
as  air)  gives  to  the  glass  of  the  receiver  is  unable  to 
communicate  so  much  motion  to  it,  as;  when  commu- 
nicated to  the  outer  air,  suffices  to  give  rise  to  an 
audible  sound  wave.  (Compare  empty  and  sand- 
loaded  tubes,  §  86.) 

In  the  preceding  §§  we  have  examined  the  pro- 
duction of  sound,  that  is,  air  waves,  by  the  vibration 
of  rods,  strings,  membranes,  plates,  &c.,  and  it  is  rare 
that  a  sound  wave  is  neither  started  nor  controlled  by 
solid  matter.  The  singing  of  a  kettle  depends  indeed 


Vibrations  of  Gases.  105 

upon  the  collapse  of  strings  of  steam  bubbles  in  water, 
and  a  few  other  instances  may  be  adduced :  but  it  not 
unfrequently  happens  that,  although  solid  matter  de- 
termines the  sound  wave,  it  does  not  itself  participate 
in  the  motion  its  presence  causes.  Pure  wind  instru- 
ments, as  the  flute,  are  examples  of  this.  It  must  be 
allowed  that  there  is  great  ignorance  concerning  the 
motion  of  the  air  at  the  mouth  of  a  tube  over  which  a 
lateral  current  is  passing.  It  appears  that  at  the  first 
instance  air  is  caught  by  the  edge  and  sent  down  the 
tube  as  a  condensation.  This  returns  after  reflexion 
from  the  bottom  at  an  interval  dependent  upon  the 
length  of  the  tube,  reappears  at  the  mouth  as  a  con- 
densation, and  passes  out  of  the  mouth  pushing  away 
the  air  current.  The  wave  of  condensation,  however, 
on  leaving  the  tube's  mouth,  leaves  a  region  of  rare- 
faction behind  it  into  which  the  air  current  is  pushed. 
The  latter  again  partly  enters  the  tube,  and  sends  down 
it  a  wave  of  compression.  There  is  accordingly  a 
kind  of  vibration  of  the  air  current  towards  and  away 
from  the  tube's  mouth,  which  vibration  is  governed  by 
the  time  required  for  the  wave  to  travel  to  and  fro  in 
the  tube. 

Accordingly  of  two  tubes  closed  at  the  bottom, 
one  of  which  is  twice  as  long  as  the  other,  the  longer 
will  give  the  lower  octave  of  the  shorter,  that  is,  a 
wave  system  of  twice  the  length,  of  doiuVe  the  time 
interval,  of  half  the  rate  of  recurrence  (pitch). 

§  97.  Let  us  confirm  this  as  follows.  Take  any 
tuning-fork  the  number  of  whose  vibrations  per  second 
is  known,  say  c,  which  makes  suppose  256  complete 
vibrations  in  a  second.  From  §  79  it  appears  that 


io6 


Practical  Physics. 


wave  length  in  feet  = 


no.  of  feet  travelled  in  i  second 


FIG.  64. 


no.  of  waves  generated  in  i  sec. 
In  this  case  therefore  =  VV\°  =  4  ft. 
3*6  in.  Take  now  a  tube  open  at 
both  ends  and  about  \  inch  diameter, 
plunge  the  lower  end  into  water,  and 
holding  the  sounding  fork  above  it 
move  the  tube  up  and  down  till  the 
sound  of  the  fork  is  greatly  and  sud- 
denly increased.  Measure  the  length 
of  the  tube  from  the  open  end  to 
the  level  of  the  water,  and  it  will  be 
found  to  be  about  i  foot  0*9  in.  Cut  eight  or  ten  tubes 
of  exactly  this  length,  and  grind  their  ends  flat  on  a  wet 
sandstone  or  the  side  of  a  grindstone.  Prepare  some 
glass,  metal,  wood,  or  cork  discs  the  size  of  the 
outside  measurement  of  the  tube,  and  some  pieces  of 
vulcanised  caoutchouc  tubing  about  i  in.  long  and 
rather  less  in  diameter  than  the  tubes.  When  such  a 
disc  is  inserted  into  the  caoutchouc  and  the  latter  is 
drawn  on  to  the  glass  tube,  the  tube  is  of  course  closed 
at  one  end.  Two  tubes  joined  by  a  piece  of  caout- 
chouc form  an  open  tube  of  double  length  and  so  on. 
It  is  clear  that  if  we  denote  a  region  of  maximum 
motion  by  a  bundle  of  horizontal  lines,  and  node  by  a 
vertical  dotted  line,  we  have  in  a  tube  open  at  one  end 
the  following  condition  (fig.  65)  when  the  tube  is  sound- 
ifi£  its  fundamental  note.  If  we 
attach  another  unit  length  to  the  tube, 
it  refuses  to  sound,  because  to  do  so 
would  necessitate  a  region  of  maxi- 
mum  motion  at  the  bottom,  an 


FIG.  63. 


Closed  and  Open  Tubes.  107 

evident  impossibility.  But  a  tube  of  3  units  length  will 
sound,  and  so  will  all  odd  multiples  of  the  unit  (fig.  66) 
tube.  Further,  if  we  examine  what  different  forks  will 
resound  to  the  same  tube  close  at  one  end,  we  find  that 

FIG.  66. 


a  fork  giving  rise  to  three  times  the  number  of  vibrations, 
one  giving  rise  to  5  times,  FlG.  67> 

7  times,  and  so  on,  will  re-  . — 

sound  (fig.  67),  while  no  ' ^ 

even  number  multiple  of  j —  1 — 

the  vibrations  (submul-  ' i ' ^ 

tiplesofwavelengths)will  i p — j 1 1 — 

do  so,  for  they  necessitate  ' s ' ~ : ^ 

maximum  motion  at  the    \ = i — i — • — i — • — § 

=       i     =  =      ;     = 

bottom.     The  first  over- 
tone, sometimes  called  '  harmonic/  got  by  blowing 
with  violence  across  the  open  end  of  a  tube  closed  at 
the  bottom,  has  therefore  \  wave  length  of  the  fun- 
damental, the  second  |,  and  so  on. 

Take  now  a  second  tube  of  the  same  length  as  the 
first,  also  closed  at  the  bottom,  and  FlG  68 

fasten  the  closed  ends  together.  The  g r ^ 

second  tube  will  take  up  the  vibra-   ^ — 
tions  of  the  same  fork.    The  double  diaphragm  in  the 
middle  may  be  withdrawn,  for  the  pressure  on  it  from 
one  side  is  always  equal  to  that  on  the  other ;  so  that 
a  tube  open  at  both  ends  must  be  twice  as  long  as  a 


io8  Practical  Physics. 

tube  closed  at  one  end  to  sound  the  same  note.     In 
the  former  case  an  automatic  node  is  formed  in  the 
FIG.  69.  middle.      Three    unit    lengths   of 

H —  — ff     tube  refuse  to  sound  to  the  same 

555 : ^  fork,  because  the  wave  length  being 
the  same,  there  would  be  a  node  at  an  open  end  if 
there  were  maximum  motion  at  the  other,  whereas 
there  must  obviously  always  be  maximum  motion  at 
an  open  end.  A  length  of  4,  6,  8,  &c.  units  will 
resound, 

Or,  if  (fig.  70)  we  take  the  first  open  tube  which  re- 

FIG.  70. 


sounds  to  the  fork  as  the  unit  length,  all  open  tubes  which 

FIG.  71. 


are  multiples  of  this  length  will  resound.     And  in  the 
same  manner  as  before,  on  examining  what  forks  resound 


Nodes  in  Open  Tubes.  109 

to  the  same  open 'tube  (fig.  71),  we  find  that  they  are  all 
the  forks  whose  vibrating  numbers  are  multiples  (or 
wave's-length  submultiples)  of  the  lowest.  This  series 
includes,  therefore,  all  the  octaves  of  the  lowest  fork. 

§  98.  The  node  or  nodes  in  an  open  FlG>  72> 
tube,  and  the  regions  of  maximum  motion, 
can  be  examined  in  an  open  organ  pipe. 
Such  a  pipe  has  one  free  open  end,  but 
the  end  where  the  air  current  vibrates 
is  not  so  free.  A  little  tambour,  covered 
loosely  with  tissue  paper,  will  rustle  at 
the  top  and  bottom  of  the  tube,  but 
remain  tranquil  near  the  middle. 

A  node  being  a  place  where  the  change 
of  density  is  greatest,  and  half-way  between 
the  nodes  being  where  there  is  least 
change  of  density  though  greatest  motion, 
the  existence  of  one  or  other  condition  can  be 
shown  by  the  effect  on  flames  as  follows.  Let 
an  open  organ  pipe  (fig.  73)  have  three  holes  cut 
along  one  side,  at  ^,  ^,  f  the  pipe's  length  from  the 
end.  These  holes  are  covered  with  gold-beater's 
skin,  and  the  skin  is  covered  by  a  little  box  in 
each  instance.  Into  all  three  of  these  side  cham- 
bers coal  gas  is  led,  and  to  each  there  is  a  small  jet 
at  which  the  gas  can  be  burnt.  The  jets  are  set 
burning  at  all  three  places.  When  the  fundamental 
note  is  sounded  the  central  jet  alone  is  extinguished. 
For  the  alternate  compression  and  rarefaction  of  the 
air  at  the  node  which  is  formed  there  moves  the 
membrane  in  and  out,  and  so  puts  out  the  flame. 
On  sounding  the  next  harmonic,  that  is,  the  higher 


no  Practical  Physics. 

octave,  nodes  are  formed  at  the  first  and  third  gas 

FIG.  73. 


I       1 

jets,  and  these  are  extinguished  while  the  central 
one  now  continues  burning.  It  is  evident  that  the 
first  experiment  only  shows  a  differential  effect,  since 
the  positions  of  the  jets  are  not  the  regions  of  greatest 
motion,  and  therefore  are  not  free  from  variation  in 
pressure. 

§  99.  Resonance. — The  acceptance  by  a  tube  of  a 
system  of  waves  of  a  sonorous  body  is  called  resonance; 
FIG  and  for  narrow  tubes  the 

relationship  established 
in  §§  97,  98,  holds  good. 
But  with  wider  tubes, 
even  when  cylindrical,  but 
more  markedly  if  of  irre- 
gular shape,  the  relation- 
ship between  the  sound 
wave  and  the  vessel  measurements  is  not  so  obvious. 

Thus  a  wider  cylinder  will  present  a  possibly 
longer  path  by  dint  of  reflexion,  so  that  such  a  tube 
will  also  sound  to  a  graver  fork,  and,  indeed,  may 
sound  more  fully  to  a  graver  fork,  for,  by  repeated 
reflexion,  it  can  furnish  a  great  variety  of  paths  of  the 
required  greater  length. 

Let  us  next  employ  the  resonant  cavity  to  measure 


Resonance.  1 1 1 

the  relative  rate's  at  which  sound  travels  in  different 
gases,  and  so  confirm  the  formula 


z/oc 


Fill  a  tube  so  far  with  water  that  it  resounds  to  a 
given  fork.  Lead  a  current  of  carbonic  acid  gently  to 
the  surface  of  the  water,  so  that  the  air  may  be  ex- 
pelled by  displacement.  The  tube  of  carbonic  acid 
no  longer  resounds  to  the  fork,  but  it  does  so  if  water 
be  poured  in  so  as  to  shorten  the  resonant  column. 
This  shows  that  for  sound  to  reach  from  end  to  end 
(and  back  again)  in  the  same  time  in  two  columns, 
one  of  air  and  the  other  of  carbonic  acid,  the  carbonic 
acid  column  must  be  the  shortest,  or,  in  other  words, 
the  sound  travels  fastest  through  air.  If,  on  the  other 
hand,  a  tube  be  taken  closed  at  one  end,  inverted,  and 
filled  by  displacement  by  hydrogen  or  coal  gas,  a  fork 
which  resounds  to  this  tube  will  do  so,  if  the  gas  is 
replaced  by  air,  only  when  the  column  is  shortened.  A 
copper  tube  which  resounds  to  a  fork  when  heated, 
does  not  do  so  when  cooled,  unless  virtually  shortened. 
All  these  experiments  show  that  sound  travels  more 
slowly  through  a  gas  of  greater  density,  if  the  elasticity 
remains  unchanged,  as  is  the  case  in  all  these  experi- 
ments, since  the  gas  has  the  same  elasticity  as  the  air. 
When  a  gas  is  compressed  its  density  and  elasticity 
increase  together,  and  accordingly  no  change  in  velo- 
city occurs.  This  is  the  condition  of  change  brought 
about  by  variation  in  barometric  pressure ;  such  a 
variation  accordingly  is  not  accompanied  by  any 
change  in  sound  velocity.  The  acquirement,  however, 


112  Practical  Physics. 

of  aqueous  vapour,  which  diminishes  density  without 
affecting  elasticity,  increases  velocity. 

§  100.  Longitudinal  vibrations  of  liquids  and 
solids. — Although  the  transverse  vibrations  of  solids  are 
accompanied  and  caused  by  states  of  compression  or 
rarefaction,  or  both,  these  states  do  not  pursue  the  same 
course  as  the  vibration  itself  does.  Both  solids  and 
liquids  are,  however,  capable  of  such  compression  and 
F  f  rarefaction,  and  so  of  convey- 

ing sound  waves  in  the  same 
sense  that  air  does.  This 
is  shown  in  the  case  of 
liquids,  by  fastening  a  tube 
containing  water,  mercury, 
or  other  liquid,  fig.  75,  on 

-i      to   a    sounding-board,   and 

plunging  into  the  top  of  the 

liquid  a  cork  cone  fastened  to  the  end  of  a  tuning- 
fork.  The  sound  heard  proves  that  the  wave  of 
condensation  travels  through  the  water.  The  actual 
velocity  of  sound  through  water  is  about  four  times 
that  through  air.  The  actual  comparison  between 
the  rate  of  a  wave  through  air  and  through  a  solid  is 
established  as  follows  :  a  tuning-fork  is  held  over  a 
narrow  cylinder  into  which  water  is  poured  until 
the  maximum  resonance  is  reached.  A  solid  cylin- 
drical rod,  say  of  oak,  is  held  in  the  middle  between 
finger  and  thumb,  and  one  of  the  free  ends  is  rubbed 
longitudinally  towards  the  middle  with  a  piece  of 
leather  covered  with  powdered  resin ;  a  pretty  clear 
note  is  thus  produced,  the  origin  of  which  is  the 
breaking  of  the  brittle  resin  powder  at  a  certain 


- 

Longitudinal  Vibrations  of  Solids.      1 1 3 

degree  of  strain,  setting  up  of  a  wave  of  altered 
density,  which,  after  being  reflected  at  the  further  end, 
returns  to  the  end  being  rubbed.  It  then  beats  and 
pulls  the  air,  giving  rise  to  an  audible  air  wave  ;  the 
time  required  for  the  next  solid  wave  to  pass  down 
and  up :  that  is,  the  time  interval  between  two  solid 
waves  (and  therefore  between  the  two  air  waves  to 
which  they  give  rise),  is  directly  proportional  to  the 
length  of  path  (twice  length  of  rod)  and  inversely  pro- 
portional to  rate  of  travelling.  If  the  rod  be  so  cut 
down  that  it  gives  the  same  note  as  the  tuning-fork 
and  its  resonant  column,  it  follows  that  the  solid 
wave  takes  the  same  time  to  travel  from  end  to  end 
of  the  rod  as  the  air  wave  takes  to  travel  from  the 
mouth  of  the  jar  to  the  water  surface  and  back  again ; 
for  it  must  be  borne  in  mind  that  a  rod  vibrating  as 
above  described  resembles  a  pipe  open  at  both  ends, 
which  (§97)  has  been  shown  to  have  twice  the  length 
of  the  closed  pipe  giving  the  same  note.  Thus  it  is 
found  that  if  the  air  column  resounding  to  a  given  fork 
be  6  in.  long,  an  oaken  rod  must  be  cut  down  to  about 
10  feet  to  give  the  same  note.  The  velocity  of  the  oaken 
wave  is  to  the  velocity  of  the  air  wave  as  10  feet  is  to 
twice  6  in.,  or  as  10  to  i.  A  deal  or  steel  rod  must  be 
32  times  as  long,  or,  reckoned  from  the  middle,  16 
times  as  long  as  the  similarly  vibrating  air  column. 

§  1 01.  The  comparative  rate  of  metal  waves  is 
found  in  a  similar  way,  but  wires  may  be  employed. 
The  actual  wave  lengths  can  be  traced  out  by 
the  arrangement  of  lycopodium,  if  the  waves  be 
reflected  from  the  bottom  of  a  tube,  so  that  nodes 
may  be  established.  And  this  method  enables  us 
i 


Practical  Physics. 


either  to  compare  different  solids,  using  the  same  gas 
in  the  tubes,  or  different  gases,  using  the  same  solid 
FIG.  76.  exciter.  In  fig.  76,  sup- 

pose there  are  two  rods 
of  the  same  length, 
one  of  brass  and  the 
other  of  glass,  each 
supported  in  its  middle  by  a  cork  fitting  into  the  end 
of  a  glass  tube,  the  other  end  of  which  is  closed.  If 
the  tube  be  of  the  right  length,  measured  from  the 
end  of  the  rod  to  the  bottom,  that  is,  any  multiple  of 
the  half  wave  length  of  the  note,  stationary  waves  will 
be  formed,  in  whose  nodes  the  lycopodium  accumu- 
lates. If  both  rods  are  of  glass,  and  one  tube  be 
filled  with  hydrogen,  the  waves  in  the  latter  are  found 
to  be  longer  than  those  of  the  air. 

§  102.  The  conveyance  of  sound  through  solids  is 
not  only  quicker,  but  more  perfect,  than  through  air. 
A  watch  is  heard  to  tick  when  placed  at  the  end  of  a 
deal  rod  several  yards  long,  if  the  ear  be  placed  at 
the  other  end.  A  piano  in  one  room  gives  its  vibration 
to  wooden  rods  passing  into  a  room  several  score 
yards  off,  and  will,  if  the  rod  be  connected  with  a 
sounding-board  in  the  second  room,  appear  to  be 
FIG.  77.  played  there. 

If  two  round 
tubes,  about 
3  in.  in  dia- 
meter, have 
a  membrane 
stretched 
tightly  over 
one  end  of  each,  and  a  thiead  be  fastened  to  the 


Transmission  of  Sound.    Interference.     1 1 5 

membranes  through  the  centre  by  means  of  knots 
and  a  little  wax,  the  voice  speaking  into  one  can 
be  heard  in  the  other,  though  the  thread  be  20  or  30 
yards  long,  provided  it  is  kept  moderately  stretched. 
It  may  even  be  carried  round  corners,  if  it  be  sup- 
ported at  the  corners  by  short  flexible  threads.  By 
employing  steel  wire  and  metal  membranes,  conver- 
sation can  be  heard  from  a  quarter  of  a  mile, 

§  103.  Interference  Beats. — If  a  mass  of  air  is 
acted  on  simultaneously  by  two  systems  of  waves,  it 
will  be  affected  (i)  according  to  the  relative  phases  of 
the  two  systems,  if  they  are  of  equal  length,  and  (2) 
according  to  their  lengths.  We  need  only  look  at  a 
few  cases  of  each.  Let  us  suppose  that  in  all  cases 
the  waves  have  equal  amplitudes.  First,  let  the  wave 
systems  be  of  equal  wave  length,  and  start  together. 
Fig.  78,  (i)  the  waves  aug-  FIG  7s. 

ment  one  another's  ampli-       ^        ^       ^, 
tude   throughout.      If  the    §  /  \     .  /  \      /  \     A.) 
one  system  is  ^  of  a  wave  Y/        v/       \s 

length  before  the  other,  we   a  r^"\_y'x~\ ;^~\^>(*} 

get  (2),  and  so  on.     A  dif-   ^  ^^      ^^       ^^ 
ference   of  J  wave   length   * 

gives  perfect  extinction.    If  I         -          —        —  '^ 
the  difference  be  still  further   I 

3 ^ , ^- — -~^/0> 

increased,    the   joint  wave   » "" 

system  increases  in  ampli-   I" — "'" 

tude,  and  therefore  in  loud-   r      /">      ./~~\.     /""Nirt 

8    \.^/  \^/  \    / 

ness,  until  f  (9)  is  reached,  ^.          X-N        r\ 

which  is  the  same   as  (i).  | .     /  \      /  \     /  V} 
To  show  this,  a  tube,  shown  *  \J       \J       \J 
in  fig.  79,  is  used.   A  caout- 
1 2 


Ii6  Practical  Physics. 

chouc  tube  containing  a  whistle  is  fastened  to  a.   The 
sound  waves  are  divided  at  b,  half  each  wave,  that  is, 
FIG.  79.  condensation  of  half  am- 

plitude, and  rarefaction  of 
half  amplitude,  goes  to  the 
right,  and  half  to  the  left. 
If  their  paths  be  equal, 
they  meet  again  as  they  parted,  and  augment  one 
another's  amplitude,  and  so  restore  the  full  sound. 
But  if  the  movable  loop,  //,  be  drawn  out,  so  that 
the  additional  path  of  the  left  limb  of  the  wave  is 
equal  to  half  the  wave  length,  the  two  wave  systems 
will  encounter  one  another  at  <:,  in  opposite  phases, 
as  in  case  (5),  fig.  78,  and  the  two  wave  systems  pro- 
duce silence.  The  gradual  extinction  of  the  sound, 
and  its  gradual  restoration,  as  the  sliding  piece  is 
pulled  twice  as  far  out,  shows  that  all  the  cases  of 
fig  78  are  passed  through. 

§  104.  In  the  next  place,  considei  the  effect  which 
two  wave  systems  have  on  one  another,  if  they  have 
some  very  simple  relation  in  their  wave-lengths,  say 
i  :  2,  and  suppose  (i)  that  they  start  in  the  same 
phase,  (2)  that  the  shorter  wave  is  |  a  long  wave  in 
advance,  (3)  when  the  short  one  is  f  in  advance,  and 
so  on.  Fig.  80  shows  the  effect. 

Next  let  there  be  some  other  but  integral  relation 
between  the  wave-lengths  of  two  wave  systems  which 
are  started  simultaneously,  fig.  81,  where  seven  waves 
of  one  system  are  as  long  as  6  of  the  other.  If 
they  start  together  it  follows  that  the  first  condensa- 
tions will  travel  together  and  the  amplitude  will  be 
their  sum.  Condensation  No.  3  of  the  6  system  will 


Interference.  117 

be  sent  off  at  the  time  half-way  between  the  3  and  the  4 
of  the  7  system,  that  is,  at  the  time  when  a  maximum 


FIG.  80. 


3,  "//      \^\/_\V//       \V    /      \  sf/      \Y>y"" 


f  \J 
f 


fasf;  f  asl;  f  asf;  J  as  f ;  |  as  f. 

rarefaction  of  that  system  is  evolved.  These  will 
annihilate  one  another.  When  the  6th  of  the  6  sys- 
tem is  sent  off,  the  7th  of  the  7  system  will  be  sent 
off  also,  and  these  will  assist  one  another. 

FIG.  81. 


A  burst  of  sound  called  a  beat  is  heard  when  the 
region  of  augmentation  reaches  the  ear ;  these  are 
alternated  with  periods  of  comparative  silence. 

§  105.  Interference  is  shown  experimentally  by 
the  tuning-fork.  If  such  a  sounding  fork  be  held  over 
its  resonance  tube  horizontally  and  gradually  revolved, 


n8  Practical  Physics. 

four  positions  are  found  in  which  the  sound  is  almost 
extinguished,  and  these  positions  are  when  the  side 
faces  of  the  fork  are  at  about  45°  with  the  resonance 
tube.  In  the  corresponding  lines  the  wave  of  rarefac- 
tion from  one  prong  cuts  the  wave  of  condensation 
from  the  other,  and  mutual  destruction  ensues.  If 
FlG  82f  when  the  fork  is  in  this  position 

one  of  the  prongs  be  surrounded 
kv  a  paper  tube,  so  as  to  absorb 
its  vibrations,  the  sound  of  the 
other  prong  is  restored.  So 
when  the  fundamental  note  of 
the  vibrating  plate  (§  95)  is 
sounding,  it  is  weakened  from  the  circumstance  that 
neighbouring  segments  are  always  in  opposite  phases. 
If  two  pieces  of  cardboard  cut  to  the  shape  of  two 
segments  be  held  over  two  opposite  segments,  so  as  to 
kill  their  sound,  the  other  two  segments  sound  louder. 
On  setting  the  plate  in  any  other  condition  of  vibraticn 
and  passing  the  palm  of  the  hand  close  over  its  surface 
without  touching,  its  effect  in  lessening  the  interference 
is  made  audible. 

It  follows  from  §  104  that  the  beats,  being  condi- 
tions of  density,  travel  through  the  air  at  the  same 
rate  as  the  waves  whose  interference  causes  them.  The 
more  nearly  notes  are  in  unison,  the  longer  the  interval 
in  time  and  space  between  the  beats.  Practically,  the 
audibility  of  beats  is  of  great  importance  in  estimating 
the  difference  between  notes  in  near  accord ;  and  the 
elimination  of  beats  is  a  guide  in  bringing  notes  to 
strict  accord.  For  the  number  of  beats  which  two 
notes  sounding  together  give  in  a  second  is  the  diffe- 


Interference.  1 19 

rence  between  the  numbers  of  their  individual  vibra- 
tions in  a  second.  Thus  in  §  89,  where  the  bridge  of 
the  monocord  was  moved  till  unison  was  obtained, 
perfect  unison  is  preceded  by  beats  which  get  less 
and  less  frequent  till  they  cease  to  be  distinguishable. 
On  continuing  to  move  the  bridge  in  the  same  direc- 
tion they  become  audible  again,  and  as  the  bridge  is 
moved  the  rapidity  is  increased — they  get  too  nume- 
rous to  count,  until,  when  they  reach  about  32  in  a 
second,  their  existence  is  perceived  as  discord. 

Beats  are  readily  produced  between  forks  in  unison 
by  loading  one  prong  of  one  with  a  piece  of  metal 
stuck  on  with  wax.  The  beats  become  more  frequent 
as  the  metal  is  fixed  nearer  to  the  end,  and  also  as  its 
weight  is  increased. 

§  1 06.  Small  flames  burning  inside  open  tubes 
often,  by  establishing  currents,  blow  them-  FIG  g 
selves  partially  out,  so  that  full  combustion 
ceases ;  the  current  stops  and  the  flame  strikes 
back ;  this  gives  rise  to  an  air  wave,  according 
to  the  length  of  the  tube,  in  such  away  that  the 
advent  of  the  air  wave  at  the  flame  causes  a 
flicker  of  the  flame,  and  the  flicker  of  the 
flame  causes  an  air  wave.  Two  such  tubes, 
if  alike,  will  sing  in  unison,  but  by  sliding  up  a  paper 
tube  surrounding  one,  its  tube  is  lengthened,  a  lower 
note  results  and  beats  are  heard.  That  such  a  singing 
flame  palpitates  is  seen  by  moving  the  head  quickly 
from  side  to  side  while  looking  at  it  or  by  focussing 
it  by  a  convex  mirror  upon  a  screen  and  turning  the 
mirror  quickly  but  slightly  on  a  vertical  axis.  The 
image  appears  then  in  different  places  when  of  dif- 


I2O  Practical  Physics. 

ferent  sizes,  so  that  a  uniformly  jagged  appearance 
results. 

§  107.  Sinuosities.-— The  above  method  of  making 
palpitation  visible  is  only  one  instance  of  the  device 
by  which  a  to-and-fro  motion  is  converted  into  a  wavy 
or  sinuous  one  by  combining  it  with  motion  of  trans- 
lation. If  a  piece  of  elastic  wire  is  fastened  to  a  prong 
of  a  tuning-fork  and  held  in  such  a  way  that  when  the 
fork  sounds  the  wire  scratches  lampblack  off  a  sheet 
of  glass,  the  scratch  will  be  a  line.  But  if  either  the 
fork  is  drawn  along  or  the  glass  shifted,  a  sinuous  line 
is  laid  bare.  If  the  relative  movement  endures  for  a 
second,  whether  that  movement  be  fast  or  slow,  there 
will  be  as  many  crests  on  one  side  of  the  sinuosity  as 
there  were  complete  vibrations.  Use  has  been  made 
FIG.  84.  of  this  method  for  regu- 

lating forks  to  agree  with 
a  normal  fork.  Both 
forks  are  provided  with 
little  styles  of  bristles. 
These  delay  the  vibration  a  little,  but  affect  both 
forks  alike.  The  styles  rest  upon  a  cylinder  which 
is  covered  with  lampblack  and  can  be  turned  on 
a  horizontal  axis  which  is  a  screw.  In  this  way 
the  cylinder  advances  as  it  turns,  and  the  sinuosities 
take  a  spiral  form.  The  number  of  waves  between 
two  lines  parallel  to  the  axis  is  counted,  and  the  fork 
under  trial  filed  accordingly  (see  §  85). 

§  1 08.  Effect  of  motion  of  the  source  of  sound. 
— If  we  were  to  begin  to  move  away  from  a  source  of 
sound  the  moment  it  began  to  give  forth  n  vibrations 
per  second,  and  were  to  move  at  the  rate  of  1,100  feet 


Motion  of  a  Source  of  Sound.         121 

second,  it  is  clear  that  the  sound  would  never  over- 
take us.  If  we  were  to  move  at  the  rate  of  550  feet  a 
second,  at  the  end  of  the  second  we  should  have  been 

overtaken  by  -  sound  waves,  because  the  -th  sound 

wave  would  be  at  550  from  the  source.     Hearing  - 

sound  waves  in  a  second,  we  should  hear  the  octave 
lower  than  we  should  have  done  had  we  remained 
at  rest.  And  inversely,  if  we  started  at  a  distance  of 
1,100  feet  from  the  source  of  sound,  and  began 
moving  towards  the  source  of  sound  at  the  rate  of 
1,100  feet  a  second  the  moment  the  source  of  sound 
began  giving  off  ;/  vibrations,  we  should  hear  nothing 
in  the  first  half-second,  or  550  feet.  Then  we  should 
hear  the  whole  n  vibrations  in  the  next  half-second, 
or  550  feet,  and  reach  the  sounding  body  just  as  it 
had  completed  its  #th  vibration.  Evidently,  therefore, 
the  pitch  of  the  note  which  we  should  hear  would  be 
an  octave  higher  than  it  would  have  been  if  we  had  re- 
mained at  rest.  It  is  also  clear  that  this  change  of  pitch 
by  motion  is  the  same  whether  we  move  or  whether  the 
source  of  sound  does  so.  This  is  shown  by  fastening 
a  whistle  to  the  end  of  a  long  caoutchouc  tube,  and 
whirling  the  tube  round  while  the  whistle  is  sounding. 
To  a  person  standing  at  some  distance  the  pitch  of 
the  note  is  heard  to  become  graver  as  the  whistle  re- 
cedes, and  shriller  as  it  advances  towards  him. 

Sympathy.  —  If  two  solid  bodies,  such  as  two 
strings  or  taning-forks,  are  capable  of  giving  out  the 
same  note  when  sounded,  the  sounding  of  one  alone 
will  cause  the  other  to .  sound  if  the  two  be  in  con- 


122  Practical  Physics. 

nection  by  any  elastic  medium.  Thus  if  two  tuning- 
forks  placed  side  by  side,  facing  one  another,  be 
related  as  a  note  and  its  octave,  and  a  third  fork  in 
unison  with  one  of  them  be  sounded  and  placed 
between  them  at  the  same  distance  from  each,  the 
unison  fork  alone  will  sound.  A  pellet  of  wax  hung 
resting  against  this  one  will  be  thrown  off,  while  a 
similar  pellet  attached  to  the  other  will  remain  at  rest. 
This  may  be  regarded  as  an  absorption  of  vibration. 

These  experiments  are  interesting  on  account  of 
their  supposed  relationship  to  similar  absorption  of 
light  rays,  but  are  here  chiefly  noteworthy  inasmuch 
as  they  confirm  the  assertion  that  there  is  little  change 
in  the  wave  length  in  its  passage  through  the  air. 

§  109.  Approach  caused  by  vibration. — The  air  in 
the  neighbourhood  of  a  vibrating  body  is  on  the  whole 
somewhat  less  dense  than  when  the  body  is  at  rest. 
If  a  mixture  of  lycopodium  and  sand  be  scattered  on 
a  vibrating  plate  (§95)  which  has  broken  up  into 
FIG.  85.  segments  (fig.  85),  while  the  sand  col- 

„ ,     lects  on  those  lines  where  there   is 

least  motion,  the  lycopodium  collects 
in  the  complementary  regions  where 
the  motion  is  greatest.  On  examining 
those  little  heaps  of  powder  the  par- 
ticles are  seen  to  enter  the  heaps  at 
the  base,  rise  in  the  middle,  and  roll  down  the  slope, 
showing  that  there  is  an  inrush  of  air  laterally  to 
supply  partial  rarefaction.  Further,  if  one  limb 
of  a  large  tuning-fork  be  fastened  air-tight  in  a  tube 
(fig.  86),  from  which  a  capillary  tube  leads  into  water, 
when  the  other  limb  is  bowed  the  water  sinks  in  the 


Approach  caused  by  Vibration.         123 


FIG.  86. 


capillary  as  though   a  vibrating  fork  occupied  more 
room  than  one  at  rest. 

Finally,  a  series  of  air  waves 
from  a  fork  on  striking  on  a  lightly 
suspended  surface,  either  smooth 
or  rough,  cause  the  surface  to 
approach  the  fork ;  or  if  the  sur- 
face be  fixed  and  the  fork  mov- 
able, the  fork  approaches  the 
surface.  This  is  the  case  whether 

the  surface  be  smooth  or  rough.          - 

A   toy  caoutchouc  ball   floating         I  [ 

on  clean  water  shows  this  effect  to 

perfection. 

§110.  The  Phonograph.— By  speaking  on  to  a 
stretched  membrane,  the  other  side  of  which  carries  a 
style,  and  moving  a  smoked  glass  surface  at  a  uniform 
rate  across  the  style,  a  permanent  record  is  obtained 
of  the  vibrations  corresponding  to  the  words  uttered. 
The  logograph  is  a  device  of  this  kind.  In  the 
phonograph  not  only  is  a  similar  record  preserved,  but 
it  is  of  such  a  nature  as  to  be  usable  in  the  reproduc- 
tion of  the  sounds  and  articulate  words.  A  spiral 
groove  is  cut  in  a  revolving  drum  (§  107,  fig.  84), 
which  turns  on  a  screw  axis  of  the  same  pitch  as  the 
groove.  Tinfoil  is  smoothly  rolled  upon  this,  so  that 
there  is  a  spiral  worm  cavity.  A  little  drum,  whose 
sides  are  of  wood  and  whose  membrane  is  thin  sheet 
iron,  has  a  style  fixed  to  its  centre  outwards,  and  this 
can  be  brought  and  fixed  so  that  the  style  just  touches 
the  foil.  On  turning  the  cylinder  round  and  speaking 
into  the  drum,  the  style  makes  a  series  of  indentations 


124  Practical  Physics. 

on  the  foil.  On  passing  this  series  of  indentations 
beneath  the  style  of  the  same  drum,  or  better,  beneath 
that  of  a  drum  made  of  paper,  the  style  enters  the 
cavities  which  the  first  one  made,  and  sets  its  drum  in 
vibration,  which  thus  reproduces  the  sounds  which 
the  first  drum  received.  The  complex  vibrations  of 
part-singing  can  be  registered  and  reproduced. 


APPENDIX. 


use  of  this  device  for 
FIG  87. 


~wo\ 


§  in.  The   Vernier. -The 

getting  exact  measures  of 
distances,  heights,  and 
angles,  depends  upon  the 
fact  that  it  is  easier  to  per- 
ceive exact  coincidence  in 
position  than  to  estimate 
exactly  a  difference  of  po- 
sition. A  vernier  is  a  small 
scale  sliding  edge  to  edge 
with  the  main  scale,  and 
having  its  divisions  a  little 
further  apart  than  those 
of  the  main  scale.  If  the 
object  is  to  read  to  tenths 
of  the  divisions  of  the 
main  scale,  the  length  of 
the  vernier  is  eleven  of  the 
divisions  of  the  main  scale, 
and  this  length  is  divided 
into  ten  equal  parts.  Each 
division  of  the  vernier  is 
i~  as  long  as  a  division 
of  the  main  scale.  If  the 
main  scale  is  numbered  from  below  upwards,  the  vernier 
is  numbered  from  above  downwards,  its  top  being  marked 


89 


V 

10  Ve.  =  11  Sc, 


126  Practical  Physics. 

o.  Thus  let  it  be  required  to  determine  the  height  of  the 
line  H,  fig.  87,  which  falls  between  the  97th  and  98th 
divisions  on  the  scale  S.  Push  up  the  vernier  V  till  its  top 
or  zero  line  coincides  with  H.  Look  down  the  two 
scales  and  you  see  that  89  very  nearly  coincides  with  8  ; 
assume  that  it  does  so.  The  height  of  H  is  97  +x  scale 
divisions,  and  x  is  of  such  a  length  that  .*•+  8  scale  divi- 
sions are  equal  to  8  vernier  divisions,  or  to  8  +  ^  scale 
divisions  ;  that  is,  x  +  8  =  8  +  ~,  whence  x  is  ~  of  a  scale 
division  and  the  height  of  H  is  97  +  ~. 

The  divisions  on  the  vernier  of  a  sextant  are 
generally  f£  of  the  divisions  on  the  main  scale ; 
the  latter  are  arcs  representing  20  minutes  or  \  of  a 
degree :  the  vernier  enables  reading  to  be  taken  of  ~  of  \ 
of  a  degree,  or  to  one  minute. 

§  112.  Parchment  paper. — Mix  slowly  two  pints  of 
commercial  oil  of  vitriol  with  one  pint  of  water  and  cool 
to  about  15°.  Pour  into  a  shallow  basin,  and  drag 
through  it  a  sheet  of  unsized  paper  (Swedish  filtering 
paper  is  good)  at  such  a  rate  that  each  part  of  the  paper 
is  in  contact  with  the  liquid  for  about  five  seconds  ; 
plunge  the  paper  immediately  into  a  pail  of  water  and 
thence  after  a  few  minutes  into  a  basin  under  the  tap. 
After  a  quarter  of  an  hour's  rinsing  a  drop  or  two  of 
ammonia  may  be  added  and  the  rinsing  continued. 
The  paper  should  be  kept  moist.  A  strip  of  this  paper 
an  inch  wide  should  support  at  least  twenty  pounds. 

§  113.  Hints  on  glass  working-. — Perhaps  the 
following  few  hints  on  working  in  glass  may  be  useful 
for  the  construction  of  some  of  the  apparatus  described. 

To  cut  a  glass  tube. — Lay  the  tube  over  the  edge 
of  the  table,  and  tilt  it  a  very  little,  so  that  the  place 
where  it  has  to  be  cut  rests  on  the  edge  of  the  table. 
Hold  the  tube  close  to  this  place,  and  give  one  long  and 
Steady  cut  with  a  three-cornered  file,  guiding  the  file  with 


Glass   Working.  127 

the  thumb-nail,  If  the  tube  is  very  thick  in  the  glass  as 
well  as  in  diameter,  repeat  two  or  three  times  in  the 
same  place,  but  don't  saw.  Hold  it  horizontally  on  both 
sides  before  the  chest,  with  the  cut  towards  you  ;  pull, 
and  bend  as  liitle  as  possible.  The  less  the  bending  the 
cleaner  the  cut. 

To  smooth  the  ends  of  tubes. — Tubes  which  have 
to  be  passed  through  corks,  or  connected  by  caoutchouc 
tubing,  should  have  their  ends  smoothed.  Warm  the 
end  by  passing  it  through  the  air-gas  burner,  then  hold 
it  obliquely  in  the  flame,  turning  it  till  the  edges  are 
rounded  :  this  is  seen  to  happen  soon  after  the  flame 
begins  to  be  coloured  yellow  by  the  sodium  of  the 
glass. 

To  bend  tubes. — Tubes,  unless  of  great  thickness, 
should  be  bent  with  one  motion,  unless  the  bend  is 
required  to  be  a  gradual  curve.  The  two  parts  on  either 
side  of  where  the  bend  is  to  be  are  held  as  near  as 
possible  to  the  centres  of  gravities,  lightly  with  the  same 
grip  as  a  pen  is  held,  under-handed,  thumb  upwards. 
The  region  being  gradually  warmed,  the  tube  is  held 
rather  obliquely  through  the  solid  part  of  the  flame, 
being  constantly  turned  round.  As  soon  as  the  flame 
burns  yellow  and  two  or  three  inches  of  the  tube  are 
found  to  be  soft,  the  tube  is  removed  from  the  flame  and 
bent  to  the  required  angle.  A  tube  which  has  been 
bent  so  sharply  that  there  is  a  crease  in  the  bend  is 
pretty  sure  to  break  there. 

To  close  the  end  of  a  tube. — Tubes  not  more  than 
half-inch  in  diameter  may  be  closed  over  the  simple  air- 
gas  burner.  They  should  be  softened  near  the  end  and 
the  end  pulled  off :  this  leaves  a  tail  of  glass  :  the  root  of 
the  tail  is  heated  and  again  pulled  off,  and  so  on  till  the 
tail  is  very  slender  ;  then  cut  it  off  and  heat  the  stump 
in  the  flame  :  it  will  melt  and  run  up,  making  the  end 


128  Practical  Physics. 

about  of  the  same  thickness  as  the  rest  of  the  tube.  When 
the  end  is  red-hot  it  may  be  further  smoothened  by 
removing  it  from  the  flame  and  gently  blowing  into  the 
open  end.  To  close  a  wide  thick  tube,  the  table  blow- 
pipe is  preferable. 

To  fuse  platinum  Into  a  glass  tube. — The  whole 
region  being  heated,  a  fine  blow-pipe  flame  is  made  to  play 
FIG.  88.          on  tne  point, and  when  this  is  soft  a  pla- 
tinum wire  is  stuck  to  it  and  rapidly 
pulled  away  ;  this  draws  out  a  little  tube: 
^^^     this  tube  is  cut  off  as  close  as  possible  to 
the  main  tube,  and  the  end  is  heated  till 
its  edge  shrinks  so  as  scarcely  to  project 
upon  the  main  tube.    The  platinum  wire 
is  thrust  through  the  hole,  which  it  should 
nearly  fit ;  the  glass  is  softened,  and  the 
red-hot  wire  is  worked  a  little  in  the  hole,  both  in  and 
out  and  round  about,  to  enforce  complete  contact. 

To  join  tube  to  tube,  end  to  end. — If  they  are  of 
the  same  or  nearly  the  same  diameter,  the  ends  should  be 
cut  clean  and  flat,  but  not  ground  ;  the  further  end  of  one 
tube  should  be  closed  with  a  cork.  The  ends  being 
thoroughly  and  uniformly  softened,  are  pressed  gently  to- 
gether ;  for  steadiness  the  wrists  may  be  in  contact.  The 
joint  is  allowed  to  get  sufficiently  cool  to  prevent  bending 
when  the  whole  is  held  in  one  hand.  A  pointed  flame  of 
the  blow-pipe  so  made  that  the  tube  is  not  softened  all  round 
is  applied  in  succession  to  three  or  four  points  of  the 
join,  and  air  is  gently  blown  in  at  the  open  end,  not  so  as 
to  make  a  bulb  but  so  as  to  restore  the  cylindrical  form. 
By  this  means  the  appearance  of  a  joint  is  quite  erased 
beyond  a  little  irregularity. 

If  the  tubes  are  of  very  different  diameter  the  wider 
one  should  be  drawn  out  with  much  heat  and  little 
pulling,  and  constant  rotation,  so  that  the  glass  of  the 


Glass  Working.  129 

neck  may  be  of  a  reasonable  thickness.     The  neck  being 
cut  through,  proceed  as  before. 

To  join  a  capillary  tube  to  another,  a  bulb  should  be 
blown  on  one  end  of  the  capillary  tube  and  then  broken 
and  the  edge  chipped  off  pretty  even.  The  edge  of  the 
so  formed  tube  is  allowed  to  collapse  till  it  is  of  about 
the  same  width  as  the  tube  to  be  joined,  they  are  joined 
as  before. 

To  join  tubes  end  to  side.— One  end  of  each  tube 
being  permanently  or  temporarily  closed,  a  pointed  flame 
is  directed  upon  one  side  of  the  tube          FlG-  89- 
whose  side  has  to  be  pierced,  and  by  ~          \\ 

blowing  a  gentle  elevation  is  produced  : 
this  is  increased  by  two  or  three  sub- 
sequent blowings  until  by  a  strong  puff  " 

of  breath  the   side  is  blown  through.  C? 

The  remains  of  the  thin  glass  bulb  are  U 

removed  by  pressure,  and  the  edge  of 

the  hole  rounded  in  the  flame  ;  the  edge 

of  the  other  tube  is  then  applied  and  II 

fused  on  as  above. 

A  simple  constriction  in  a  tube  is  made  by  using  a 
large  blow-pipe  flame  and  turning  the  tube  round  and 
round  without  drawing  it  out.  FIG.  90. 

A  bulb  is  blown  on  the  e  v         / 

end  of  a  tube  by  first  closing  /        ^  i 

the  end  and  letting  it  fall  together  till  a  good  mass  of 
glass  is  collected  at  the  end  which  must  FlG  9I. 

be  very  uniformly  hot  when  the  breath 
is  gently  forced  in  at  the  open  end. 

To  blow  a  bulb  on  the  middle  of 
a  tube,  one  end  of  the  tube  is  closed 
and  the  place  required  is  uniformly 
heated  and  the  ends  are  gently  pushed 
together  while  air  is  blown  in  at  the  open  end. 
K 


130 


Practical  PJiysics. 


If  it  be  required  to  blow  a  large  bulb  of  thickish  glass 
on  a  narrow  tube,  the  narrow  tube  should  be  joined  to  a 
FIG.  92.  piece  of  wider  tube  and 

the   bulb  blown   on  the 
latter. 

To  cut  sbeets  of  glass 
with  a  diamond.— The 
glass  should  be  placed 
on  a  piece  of  cloth  and 
the  cut  made  with  a 
single  stroke  towards  you, 
taking  care  to  cut  quite 
up  to  the  edge  next  you. 
The  plate  is  held  in  both 
hands  with  the  thumbs 
above  the  glass  quite  on 
the  edge,  one  on  each 
side  and  quite  close  to  the  cut.  It  is  then  bent  upwards. 
To  cut  a  round  piece  of  glass,  such  as  a  flask  or 
beaker,  a  crack  must  be  made  in  the  vessel  by  heating  a 
part  of  it  and  dropping  a  drop  of  water  on  the  heated 
part.  A  piece  of  pointed  charcoal  or  pastile  is  set  on 
fire  and  the  point  moved  a  little  in  advance  of  the  crack, 
which  follows  it,  and  may  be  directed  along  any  dry  ink 
line  previously  made  on  the  glass.  The  sharp  edge,  if  it 
be  irregular,  as  it  is  apt  to  be,  is  chopped  regular  by 
a  key,  between  the  wards  of  which  the  edge  is  placed  ; 
the  fit  should  be  good  and  only  the  edge  placed  in ;  the 
key  is  turned  outwards. 

The  end  of  a  tube  may  be  ground  off  flat  by  being 
held  against  the  flat  side  of  a  grindstone,  using  water. 
It  should  be  finished  on  a  flat  sandstone  slab.  The  end 
of  a  tube  may  be  at  once  ground  flat  on  the  slab ;  the  top 
of  the  tube  being  lightly  held  serves  as  a  pivot :  a  small 
circular  motion  is  given  to  the  lower  end. 

To  bore  a  hole  in  glass,  an  old  file  is  ground  to  a 


Etching  on  Glass.  131 

three-cornered  borer,  finished  on  the  hone  and  hardened 
by  heating  it  red-hot  and  quenching  it.  The  file  is  placed 
in  a  handle  and  worked  with  the  hand  or  inserted  in  a 
watchmaker's  drill.  The  point  to  be  bored  through  is 
kept  moistened  with  oil  of  turpentine,  and  the  glass  is 
fixed  immediately  beneath  it.  When  the  hole  is  half- 
way through,  the  plate  is  inverted  and  the  hole  met  on 
the  other  side. 

§  1 14.  To  etch  a  scale  on  glass. — Steel  millimeter 
scales  are  sold,  and  from  these  millimeter  divisions  are 
easily  transferred  to  glass.  The  glass  is  cleaned  and 
heated  and  covered  uniformly,  and  not  too  thickly,  with 
melted  beeswax  and  turpentine,  20  of  wax  to  I  of  tur- 
pentine ;  the  scale  and  the  glass  are  stuck  with  a  little 

FIG.  93. 


soft  wax  on  a  table,  as  in  fig.  93.  A  rod  about  2  feet 
long  has  two  stiff  needles  driven  through  its  ends,  and 
while  one  needle  is  placed  in  a  division  of  the  scale  the 
other  scratches  the  wax  off  the  glass  ;  and,  to  prevent  the 
scratched  lines  being  too  long,  two  straight-edges  may  be 
fastened  along  the  glass.  Figures  having  been  added 
with  a  needle-point,  the  glass  is  painted  over  with  a  solu- 
tion of  hydrofluoric  acid.  In  about  half  a  minute  the  acid 
is  washed  off  and  the  wax  removed  by  spirits  of  wine  or 
turpentine.  A  clearer  etching  is  effected  by  use  of  the 
gaseous  acid.  The  glass  is  then  supported  with  its 
marked  side  downwards  over  a  mixture  of  powdered  fluor 
spar  and  oil  of  vitriol  contained  in  a  long  leaden  trough, 
which  is  kept  for  some  hours  in  a  warm  place.  The 
liquid  acid,  and  especially  the  gaseous  acid,  is  excessively 
K  2 


132  Practical  Physics. 

poisonous,  and  the  etching  should  be  performed  where 
there  is  thorough  ventilation. 

§  115.  The  siphon  barometer. — To  make  a  siphon 
barometer,  a  piece  of  well  annealed  soft- German  or  lead 
glass,  about  42  inches  long,  £  an  inch  thick  outside 
and  \  inch  inside,  and  of  the  same  bore  at  both  ends, 
is  thoroughly  cleaned  and  dried.  The  final  drying 
is  effected  by  passing  it  to  and  fro  through  an  air- 
gas  flame  throughout  its  whole  length,  and  then  heating 
nearly  to  softening  a  spot  about  4  inches  from  one 
end.  Air  is  drawn  through  from  the  other  end.  The 
place  which  was  heated  strongest  is  now  softened  in  the 
blow-pipe  flame,  and  the  short  end,  say  3  inches,  is 
drawn  off  as  quickly  as  possible,  A  sharp  flame  is  now- 
applied  to  the  root  of  the  tail,  the  tube  being  continually 
turned  and  a  fresh  piece  drawn  off,  and  so  on.  Finally, 
the  short  and  slender  tail  is  allowed  to  fall  back  upon  the 
glass.  The  end  is  then  to  be  rather  strongly  heated  in  a 
larger  blow-pipe  flame  and  air  gently  blown  in  from  the 
other  end.  This  must  be  done  until  the  inner  surface  of 
the  closed  end  is  quite  smooth  and  dome-shaped.  The 
whole  of  the  tube  is  again  to  be  strongly  heated,  and,  a 
narrow  tube  being  passed  down  to  the  bottom,  air  is  to 
be  drawn  through  the  latter.  The  narrow  tube  being 
withdrawn,  the  barometer  tube  is  bent  in  a  smooth 
bend,  commencing  at  about  34  inches  from  the  closed 
end.  The  bend  is  so  made  that  the  shorter  and  open 
end  is  as  close  as  possible  to  the  longer  limb  and  parallel 

to  it.  The  tube  is  now 
supported  on  its  back, 
inclined  downwards  to- 
wards its  closed  end 
and  its  open  limb  up- 
wards. A  little  funnel 
has  its  tube  end  drawn  out  and  slightly  bent  down  at  its 


Siphon  Barometer.  133 

extremity ;  the  drawn-out  end  is  inserted  into  the  open 
limb  of  the  barometer  till  its  extremity  is  above  the  bend 
in  the  latter,  the  tube  of  the  funnel  having  been  previously 
so  bent  that  when  it  is  so  inserted  the  funnel  stands 
upright.  The  funnel  with  its  tube,  as  well  as  the  baro- 
meter, are  all  dry  and  warm.  Petfectly  pure  mercury  is 
heated  to  about  100°  C.  in  a  basin  and  poured  into  the 
funnel,  which  must  be  kept  well  filled.  The  drops  of 
mercury  roll  down  the  barometer  tube  and  completely 
displace  the  air.  As  soon  as  the  barometer  tube  is  filled 
to  the  bend,  the  funnel  tube  is  removed  and  the  whole 
brought  gently  to  the  vertical  position.  Should  any 
minute  air-bubbles  appear,  which  is  never  the  case  if  the 
above  directions  are  strictly  adhered  to,  the  barometer 
is  gently  turned  completely  over,  so  as  not  to  spill  mer- 
cury, and  the  closed  end  is  tapped  vertically  upon 
with  a  block  of  wood.  The  air-bubbles  rise  to  the  free 
surface.  Suppose  all  the  bubbles  to  be  got  rid  of,  the 
barometer  is  turned  upright  and  a  little  more  mercury  is 
added  to  the  open  end.  If  the  vacuum  is  perfect,  when 
the  barometer  is  gently  inclined  the  mercury  rises  to  the- 
top  with  a  sharp  click. 


134 


ELEMENTARY    EXPERIMENTS 

RELATING  TO 

SOUND    AND    WAVES. 


N.B. — The  numbers  in  brackets  in  this  list  refer  to  the  paragraphs 
of  the  list  of  Apparatus  and  Materials,  pp.  151-154. 


WAVES. 

1.  Transmission  and  Reflection  of  Transverse  Mo- 
tion in  Elastic  Cords. — An  empty  vulcanized  caoutchouc 
tube   12  feet  long  is  fastened  to  the  ceiling  at  one  end, 
and  is  held  at  the  other  in  the  hand  in  a  nearly  vertical 
position.     Strike  it  with  the  other  hand.     A  half  wave 
travels  along,  and  comes  back  reversed  (i). 

2.  Two  similar  tubes,  equally  stretched,  are  similarly 
and  simultaneously  struck  ;  rate  of  motion  of  displace- 
ment is  the  same  (i). 

3.  Stretch   one  tube  more  than  the  other,  keeping 
each  at  its  full  length.     Compare  time  of  wave  from  end 
to  end.     Compare  rate  of  wave  by  making  the  unequally 
stretched  tubes  of  equal  length  (i). 

4.  Fasten  an  empty  tube  and  a  sand-filled  tube  side  by 
side.     Stretch  equally  and  take  equal  lengths.     Compare 
rates  of  wave  motion.     Stretch  sand-filled  tube  till  the 
rates  are  equal,  taking  equal  lengths  (i). 

5.  Fasten  an  empty  and  the  sand-filled  tube  end  to 
end  and  fasten  the  end  of  one  to  the  wall.     Send  a  half 
wave  up  the  other.     Notice  change  of  rate  and  change 


Experiments  on  Transverse  Waves.      135 

of  amplitude  when  the  half  wave  passes  from  one  to 
the  other  ;  also  after  reflection  (i). 

6.  Make  the  half  wave  with  either  of  the  tubes  longer 
and  longer  by  shaking  the  end  more  slowly  until  the  front 
of  the  reflected  half  wave  meets  the  front  of  the  next 
advancing  half  wave  in  the  middle  of  the  tube.     Forma- 
tion of  node  in  the  middle.     Wave  length  equal  to  length 
of  tube.     Formation  of  one  complete  stationary  wave. 
With  half  rate  of  excitement  the  tube  swings  as  a  whole, 
and  the  wave  length  is  double  the  length  of  the  tube.     By 
quicker  motion  break  up  the  tube  into  segments  separated 
by  nodes.     Repeat  with  differently  stretched  and  loaded 
tube  (i). 

7.  Transmission    and   Reflection    of    Transverse 
Motion  in  Liquids.     Water-Waves. — Examine  motion 
of  water  in  trough  (2).     Fill  trough  nearly  full  of  water, 
place  chips  of  cork  along  edge  of  water,  depress  and 
elevate  block  (2)  at  one  end  of  trough  and  watch  the 
motion    of   the  floating  cork    chips.      Substitute  little 
beeswax  balls  mixed  with  iron  filings  'till  they  just  float 
and  place  them  at  various  depths.     Observe  the  closed 
curves  in  which  the  balls  move. 

8.  Take  the  two  circular  zinc  troughs  (3).     Nearly  fill 
with  water.      Set  the   water  swinging   (oscillating)    in 
various  ways  in  both  troughs  (a)  by  tilting  them,  pro- 
ducing a  nodal  line  in  the  middle  (b)  by  moving  up  and 
down  in  the  centre  some  light  circular  body,  such  as  an 
empty  beaker  (3).     Show,  by  counting  with  a  watch,  that 
the  number  of  times  the  water  returns  to  a  given  position 
in  a  given  time  is  greater  in  the  smaller  trough,  and  that 
the  two  numbers  are  inversely  as  the  square  roots  of  the 
troughs'  radii  or  diameters.     Show,  by  hanging  a  bullet 
from  a  thread  (3)  having  the  length  of  the  trough's  radius, 
that  the  motion  of  the  water  in  case  (&)  is,  with  both  troughs, 
at  the  same  rate  as  the  pendulum.     Examine  the  motion 


136  Practical  Physics. 

.of  the  water  in  case  (b\  and  show  that  a  nodal  ring  is 
formed  nearly  at  one-third  of  the  radius  from  the  circum- 
ference, and  that  the  vertical  motion  at  the  centre  is 
nearly  double  that  at  the  circumference.  As  the  wave's 
path  is  from  the  centre  to  the  circumference  and  back, 
show  that  the  rate  of  wave  progression  is  directly 
proportional  to  the  square  root  of  the  wave  length. 

9.  Air  Motion  in  Mass.     Vortex  Rings. — Fill  case 
(4)  with  smoke  or  chloride  of  ammonium  in  suspension. 
Hit  the  canvas  at  the  back,  and  examine  the  motion 
general  and  internal  of  the  vortex  rings.     Blow  out  a 
candle  20  feet  off.     Send  one  ring  to.  overtake  another, 
and  notice  rigidity. 

10.  Partial  Vacuum  on  Dispersion. — Balance  the 
piece  of  pasteboard  (6)  on  the  point  of  the  finger  ;  place 
the  disc  with  the  tube  over  it,  and  blow  through  the  tube. 
Notice  that  the  discs  adhere  together,  showing  that,  by  the 
dispersion  of  the  air  column  in  the  tube  when  it  meets  the 
lower  disc  and  passes  between  the  two,  the  air  is  rarefied. 

11.  Approach  caused  by  Vibration. — Float  a  toy 
air  ball  (7)  on  clear  water,  and  show  that  when  a  tuning- 
fork  which  has  been  struck  is  brought  near  it,  the  baH 
approaches  the  fork. 

12.  Connection  between  the  Volume  and   Density 
and  the  Pressure  on  or  Tension  of  a  Gas.— Mercury  is 
poured  into  the  open  end  of  the  tube  (8)  just  in  sufficient 
quantity  to  cover  the  bottom  of  the  bend.     The  air  in 
the    shorter  limb   is   then   exactly   at   the   atmospheric 
pressure.     Any  quantity  of  mercury  is  then  poured  in, 
and  the  difference  .in  height  between  the  two  columns  is 
measured.     The  pressure  to  which  the  gas  is  row  sub- 
jected   is    the    atmospheric    pressure     (for    which     the 
barometer  is  consulted)  plus  the  pressure  of  the  difference 
of  the  mercnrial  columns.     The  volume  of  the  air,  which 
may  be  considered  as  the  length  of  the  air  column  in  the 


Compression  and  Rarefaction.          137 

shorter  limb,  is  found  to  be  in  all  cases  inversely  pro- 
portional to  the  pressure. 

13.  Beat   liberated  on  the   Compression  and  ab- 
sorbed  on   the    Expansion   of  Air. — Fas' en    German 
tinder  to  the  bottom  of  the  wooden  rod  in  (9)  and,  placing 
the  closed  end  of  the  tube  on  the  table,  thrust  the  wooden 
rod  down.     After  One  or  two  thrusts  the  tinder  will  light. 
Put  a  drop  of  bisulphide  of  carbon  on  a  pellet  of  cotton 
wool  and  roll  it  in  and  out  of  the  tube,  then  thrust  the 
rod  down,  the  bisulphide  will  flash.     Clean  the  tube  and 
place  in  it  a  pellet  of  cotton  wool  moistened  with  water ; 
push  the  rod  down  to  about  a  quarter  the  length  of  the 
tube  from  the  bottom.     After  a  time  pull  it  up  suddenly. 
Clouds  of  condensed  watery  vapour  will  be  formed. 

14.  Propagation    of     Compression    and    Rarefac- 
tion through  Solids  and  liquids.— Arrange  "  solitaire  " 
balls  or  marbles  (10)  in  a  groove,  and  hit   the  row  with 
one,  two,  or  three,  noticing  the  number  which  are  sent  off 
from  the  other  end. 

15.  Strike  tuning  fork  (7)  and  hold  its  root  on  one 
end  of  a  deal  rod  (7),  and  place  a  board  (7)  on  and  off 
the  other  end.     This  shows  that  the  waves  of  compression 
and  rarefaction  travel  along  the  rod. 

1 6.  Fasten  one  end  of  the  sand-filled  tube  (i)  to  the 
ceiling.     Fasten  a  piece  of  paper  near  the  top.     Send 
a  wave  of  rarefaction  up  the  tube  by  quickly  pulling  the 
free  end. 

17.  Fill  tube   (12)   with  water.     Strike  fork  armed 
with  cork  cone  (12),  and  plunge  cone  into  water  at  top 
of  tube.    The  sound  heard  shows  that  the  wave  of  com- 
pression travels  through  the  water. 


138  Practical  Physics. 


SOUND   WAVES. 

1 8.  Propagation  and  Reflexion  of  States   of  Com- 
pression   and   Rarefaction    through  Air. — The  tubes 
( 1 3)  are  fitted  end  to  end.     A  watch  is  placed  at  such  a 
distance  from  the  ear  as  to  be  inaudible.     The  tube  is 
placed  over  the  ear  and  directed  towards  the  watch.     The 
ticking  becomes  audible. 

19.  The  tubes  (13)  are  supported  horizontally  at  an 
angle  of  90°  with  one  another.     A  watch  is  placed  at  the 
end  of  one,  and  the  ear  at  the  end  of  the  other  (the  ends 
furthest  apart),  and  screens  are  placed  between  the  ear 
and  the  watch  till  the  latter  becomes  inaudible.     A  piece 
of  cardboard  or  the  hand  or  a  flat  flame  is  placed  at  their 
contiguous  ends,  making  45°  with  each    tube.      This 
makes  the  watch  audible,  and  proves  the  law  of  reflexion. 

20.  Destruction  of  Sound  Waves. — The   tubes  (13) 
are  arranged  horizontally  end  to  end  with  an  interval  of 
half  an  inch  between.     The  watch  is  placed  at  one  end 
of  one  tube,  the  ear  at  the  other  end  of  the  other  tube, 
at  such  distances  that  the  watch  is  faintly  audible.     A 
dry  cloth  placed  between  the  tubes  does  not  destroy  the 
sound,  a  wet  one  does  ;  so  does  a  current  of  heated  air 
from  a  flame. 

21.  A  watch  is  loosely  wrapped  in  folds  of  flannel  till 
it  is  inaudible.     A  deal  rod  with  board  attached  (14)  is 
thrust  amongst  the  flannel  till  it  touches  the  watch,  which 
then  becomes  audible. 

22.  A  hand  bell  is  heated  over  an  air  gas  burner. 
At  a  certain  temperature  it  ceases  to  ring  when  stnick. 

23.  A  glass  funnel  (16)  is  stopped  at  its  neck  and 
partly  filled  with   a  solution   of  carbonate  of  sodium. 
When  struck  it  rings.     Add  a-  solution  of  tartaric  acid; 
the  effervescence  causes  a  dulness  in  the  sound. 


Sound   Waves.  139 

24.  Refraction  of  Sound.  —  A  toy  air-ball  (7)  is  filled 
with  carbonic  acid.      This    is  made  by  putting  some 
marble  into  the  flask  (17),  putting  in  the  cork,  and  then 
pouring  water  and  hydrochloric  acid  down  the  straight 
tube.     The  air-ball  is  emptied  of  air  and  tied  over  the 
end  of  the  bent  tube.     When  filled   it  is  tied  off,  and 
hung  between  the  watch  and  the  ear.     The  watch  being 
two  or  three  feet  off  and  the  ball  close  to  the  ear,  the 
loudness  of  the  watch's  ticking  is  increased. 

25.  Formation  cf  Notes.  —  The  humming-top  (18)  is 
spun  on  a  hard  surface.     A  card  is  held  against  the 
toothed  wheel.     A  note   is  produced,  which  becomes 
lower  in  pitch  as  the  top  moves  slower.     Air  is  blown 
through  ttie  tube  (18)  on  to  the  outer  and  on  to  the  inner 
ring  of  holes.     The  note  produced  by  the  former  is 
always  an  octave  higher  than  that  by  the  latter. 

26.  Transverse   Vibrations    of   Rods.  —  Verify  the 
generalisation  that  if  the  length  of  a  rod  fastened  at   one 
end  is  /,  and  its  thickness,  in  the  plane  of  vibration,  is  d, 
all  other  things  being  the  same,  the  number  n  of  vibrations 
per  second  ^or  in  a  given  time)  is  such  that 

n  ~  -p  and  n  -  d 
or 


Clamp  deal  rod  (18)  flatways  (narrow  face  up)  hori- 
zontally in  the  vice  (18)  between  two  pieces  of  wood,  so 
that  10  feet  are  free  ;  set  it  vibrating  horizontally. 
Adjust  a  pendulum  bullet  (3)  so  as  to  oscillate  with  the 
rod.  Adjust  another  bullet  so  as  to  oscillate  twice  as 
fast  as  the  first.  It  will  be  found  that  the  second  pen* 
dulum  will  keep  time  with  the  rod  (a)  if  the  rod  is  10  feet 
long  and  turned  edgeways,  (d)  if  it  is  made  seven  feet  long 
and  vibrates  flatways  (io2  =  2  x  72  nearly). 


140  Practical  Physics. 

27.  Combinations    of     Motions. — Fasten    knitting 
needle  (20)  in  vice  (19),  and  fasten  a  bright  bead  on  top 
of  needle.     View  bead  by  light  of  one   candle  or  one 
distant  window.     Strike  or  pluck  in  one  direction.     The 
bead  will  appear  a  straight  line  of  light.     While  it  is 
vibrating  hit  it  in  a  direction  at  right  angles  to  its  motion 
and  it  will  describe  a  circle  or  ellipse.     Touch  one  side 
of  it  near  the  vice  with  a  stiff  feather  and  the  ellipse  will 
open  and  shut.     Clamp  the  rectangular  rod  (20)  in  the 
same  way,  and  the  figures  obtained  are  parabolic,  or 
8-shaped.     Touch  one  side  with  the  feather  and  they 
vary. 

28.  A  bright  bead  being  fastened  to  one  end  of  the 
spring  (21)  the  other  end  is  clamped  at  various  distances 
in  the  vice,  and  various  curves  are  traced  out  by  the  bead 
on  the  free  end. 

29.  Analysis  of  Vibrations  by  Sinuosities. — Fasten 
the  tuning-forks  (7),  which  are  a  fork  and  its  octave,  in 
the  vice  (19),  clamping  them  between  two  pieces  of  wood. 
Fasten  with  beeswax  on  to  the  two  prongs  on  one  side 
two  little  styles  of  quill  cut  to  fine  flexible  points.     Soak 
a  little  cotton  wool  in  turpentine,  put  it  on  a  stone  and  set 
fire  to  it.  Hold  a  glass  plate  (22)  over  the  flame  till  one  side 
is  covered  with  lamp-black.     Set  the  two  forks  vibrating 
with  the  fiddle  bow  (22)  and  draw  the  smoked  face  of  the 
glass  across  the  styles,  waved  lines  will  be  scratched  on 
the  glass;  and  the  higher  pitched  fork  produces  twice 
as  many  waves  in  the  same  length  as  its  lower  octave 
fork. 

30.  Transverse  Vibrations   of  Strings   (Wires). — 
To  show  that  the  rate  of  vibration  of  a  stretched  string 
varies  inversely  as   its  length,  other  things  being  the 
same,  fasten  two  similar  iron  wires  to  the  wood-screws 
of  the  monochord  (23).     Pass  the  other  ends  over  the 
brass  pulleys  and  fasten  equal  weights  to  them,  say  28  Ibs., 


Vibrations  of  Strings.  141 

using  the  whole  lengths  of  the  wires  from  the  fixed  bridge 
to  the  pulleys.  Pluck  the  wires  in  the  middle,  and  the 
same  notes  will  be  given.  Insert  one  bridge  halfway 
between  the  one  pulley  and  the  bridge,  the  corresponding 
string  gives  the  octave  higher  than  the  unshortened 
string.  Insert  bridge  anywhere  in  the  other  string. 
Make  one  string  half  as  long  as  the  other,  and  the 
shorter  string  always  gives  the  higher  octave  or  twice  as 
many  vibrations  in  a  second  as  theJonger  one. 

31.  To  show  that  the  number  of  vibrations  varies 
with  the  square  root  of  the  stretching  force  or  weight, 
fasten  two  weights  over  the  pulleys  and  let  one  weight 
be  four  times  as  great  as  the  other.     The  wire  with  the 
heavier  weight  gives  the  octave  higher  than  the  one  with 
the  lighter  weight.     And  this  is  the  case  if  the  bridges 
are  inserted  anywhere,  provided  the  two  are  at  the  same 
distance  from  the  pulleys. 

32.  Combine  results  31  and  32.     That  is,  hang  any 
two  unequal  weights  from  similar  wires  over  the  pulleys, 
and  Use  the  whole  length  /of  the  more  weighted  wire  ; 
shift  the  bridge  of  the  less  weighted  wire  till  the  two  give 
the  same  note.     It  is  then  found  that  if  the  wire  A  has 
the  length  /t,  and  is  stretched  by  the  weight  wlt  and  the 
wire  B  has  the  length  /2,  and  is  stretched  by  the  weight 
iv^  then  when  there  is  unison, 


Verify  this  by  altering  the  length  of  A. 

33.  From  the  above  equation  find  out  the  weight  of  a 
lump  of  iron  which  is  fastened  to  one  wire  by  obtaining 
unison  on  shifting  either  its  bridge  or  that  of  the  other 
wire,  which  is  stretched  by  a  known  weight. 

34.  Show  that,   other  things  being  the    same,    the 
number  of  vibrations  varies  inversely  with  the  thickness 


142  Practical  Physics. 

of  the  wire.  Obtain  the  relative  thicknesses  of  two  iw>n 
wires  by  weighing  equal  lengths  of  them,  and  taking  the 
square  roots  of  their  weights  ;  vary  the  weights  which 
stretch  unequal  lengths  till  there  is  unison.  Then  find 
that  the  square  roots  of  the  stretching  forces  or  weights 
are  inversely  as  the  thicknesses.  Or  that  therefore  the 
stretching  forces  are  as  the  squares  of  the  thicknesses, 
i>.  as  the  weights  of  the  wires.  Take  equal  stretching 
forces  and  vary  the  lengths  till  there  is  unison.  Then 
find  that  the  lengths  are  inversely  as  the  thicknesses. 
That  is,  verify  the  following  :  where  n  is  the  number  of 
vibrations  per  second,  /  the  length,  s  the  stretching  force, 
d  the  thickness  of  the  wire,  and  w  the  weight  of  a  given 
length. 


or  if  there  is  unison  so  that  n^ 


or 


35.  To  obtain  the  relative  diameters  of  wires  of  dissi- 
milar metals,  weigh  equal  lengths  and  take  the  square 
roots  of  the  weights  and  divide  these  numbers  by  the 
respective  specific  gravities  of  the  metals.  The  specific 
gravity  is  got  by  dividing  the  weight  of  any  piece  of  the 


Vibrations  of  Strings.  143 

metal  by  the  amount  of  weight  it  loses  in  water  (that  is 
by  the  weight  of  an  equal  volume  of  water). 

36.  The  ordinary  musical  scale  is  as  follows  for  any 
octave  where  n  is  the  number  of  vibrations  per  second 
of  the  lowest  note  (tonic)  : — 

Tonic.     Second.      **ajor     Fourth.      Fifth.     Major       Major^      Qc^ 

n         \n          |*        *»        \n        *»        ^«         2* 

If  the  middle  C  is  taken  as  having  256  vibrations  a 
second,  the  eight  complete  notes  from  this  C  to  its  higher 
octave  are — 

CDE          F          G          A          BC' 

256     288      320      341  -3      384      426-6     480      512 

If  the  middle  C  is  taken  as  264  the  numbers  are — 

CDE          F        G         A         B         C' 

264   297   330   352   396   440   495   528 

Divide  the  monochord  (23)  scale,  whose  length  from 
the  fixed  bridge  to  the  peg  or  pulleys  is,  say,  /,  into 
intervals  of  the  lengths, 

,        8          4,        3,        2          3  8  I 

*        9'       1 '       44        3 '        5 '        ip        2 

Then  whatever  be  the  stretching  force,  these  lengths, 
when  the  moveable  bridge  is  placed  at  the  corresponding 
marks,  form  a  scale.  The  full  length  may  be  tuned  by 
turning  the  peg  or  weighting  over  the  pulley  till  it  is  in 
unison  with  a  known  fork,  say  A. 

37.  Nodes  in  Strings  and  Rods. — Slightly  stretch, 
and  rigidly  fasten  in  a  vertical  position,  the  two  ends  of 
an   empty  caoutchouc  tube  (i).     Slightly  pinch  (damp) 
the  middle  and  pluck  the  tube  at  a  quarter  from  bottom  ; 
on  taking  away  the   damping  fingers  a  node  remains 


144  Practical  Physics. 

there.    Damp  the  tube  at  one-third  and  pluck  at  one- 
sixth  from  end,  two  nodes  are  formed,  and  so  on. 

38.  Use  the  stretched  monochord  wire  instead  of  the 
tube.     Place  paper  riders  at  every  one-eighth   of  the 
wire's  length.     Touch  the  second  one  with  a  stiff  feather 
and  gently  pluck  the  wire  where  the  first  is.     The  third, 
fifth,  and  seventh  will  be  thrown  off,  while  the  second, 
fourth,  and  sixth  remain. 

39.  Fasten  a  tuning-fork  (7)  upright  in  a  vice  (19),  tie 
a  piece   of  cotton  to  the  top  of  one  prong,  prevent  its 
slipping  by  a  little  wax.     Carry  the  thread  over  a  smooth 
ring  of  wire  and  fasten  a  weighed  cardboard  tray  to  the 
other    end.      Let  the  two  prongs  of  the  fork  and    the 
thread  be  in  one  plane.     Load  the  tray,  and  move  the 
ring  to  and  from  the  fork  ;  or,  keeping  the  ring  fixed,  vary 
the  weight  till,  when  the  fork  is  bowed,  there  is  only  one 
segment,  that  is,  the  thread  swings  as  a  whole.     Keeping 
now  the  length  the  same,  make  the  weight  (reckoning  the 
tray)  only  a  quarter  as  great ;  two  segments  are  formed. 
If  the  weight  be  one-ninth  as  great,  there  will  be  three 
segments  ;  if  one-sixteenth  there  will  be  four. 

If  the  string  be  at  right  angles  to  the  fork's  two 
prongs  the  segments  formed  are  always  twice  as  numerous 
as  in  the  former  cases,  if  the  lengths  and  weights  are  the 
same  as  before. 

40.  Hold  deal  rod  (19)  upright  in  hand,  and  by  tilting 
the  hand  to  and  fro  less  or  more  rapidly,  make  one  or 
more  nodes.     Mark  the  places  of  the  nodes  and  measure 
the  segments  ;  notice  that  the  last  division  swings  free, 
and  is  less  than  half  a  segment  in  length. 

41.  Cut  (24)  a  strip  of  window  glass  about  one  inch 
wide  and  any  length  /  (about  six  inches),  and  lay  it  across 
two  parallel  strings  at  such  a  distance  apart  that  each 
string  is  a  little  less  than  a  quarter  /  from  the  end.  Fasten 
the  strings  to  the  glass  with  a  little  drop  of  wax  in  the 


Transverse  Vibrations.  145 

middle  of  the  glass.     On  hitting  the  glass  in  its  centre  a 
note  will  be  produced  resulting  from  the  formation  of  one 

segment  of  length  rather  more  than—  in  the  middle  and 
two  free  half  segments  each  rather  less  than  -.  Referring 

to  26  for  the  number  of  vibrations  of  a  rod,  and  to  36 
for  the  relative  numbers  of  vibration  in  the  gamut — 


In  the  gamut  nz  =  2#M  for  the  next  whole  note, 

o 


Similarly  for  the  next  whole  note— 


and  so  on. 

Calculate  these  lengths  and  cut  strips  of  glass  accord- 
ingly. Support  and  fix  them  with  wax  in  a  row  on  two 
horizontal  threads  making  an  angle  with  one  another. 
Compare  the  motion  of  such  bars  with  that  of  the  water 
in  a  rectangular  trough  (3)  when  the  central  line  is  ele- 
vated and  depressed. 

42.  Hold  fork  (7)  horizontally  and  bow  it ;    scatter 
sand  on  it     All  is  thrown  off.     Bow  it  near  the  root.     A 
shriller  note  is  produced,  and  some  of  the  sand  rests  in  a 
line — a  nodal  line — somewhat  less  than  £  of  the  fork's 
length  from  the  end.     Prove  by  monochord  that  the  two 
notes  are  nearly  as  I  :  9  (number  of  vibrations  per  second). 

43.  Remove  clapper  from  hand  bell  (15)  ;  fix  the  bell 
vertically  upside  down  in  vice  (19).     Hold  a  pellet  of  seal- 
ing wax,  the  size  of  a  pea,  hung  from  a  silk  thread,  against 
the  edge  of  the  bell.     Bow  the  bell,  and  move  the  pellet 
round,  finding  the  four  nodal  points  and  the  four  regions 

L 


146  Practical  Physics. 

of  greatest  motion.  Nearly  fill  the  bell  with  water  and 
bow.  Notice  regions  of  comparative  rest,  and  of  disturb- 
ance. Move  quickly  in  and  out  by  the  hands  two  oppo- 
site sides  of  an  elastic  wire  (23)  hoop.  Notice  nodes  and 
segments. 

44.  Beats. — Clamp  two   similar   tuning-forks  (7)    in 
vice  (19)  or  screw  them  into  board  (n)  or  monochord 
(23).     Load  one  near  its  root  with  a  half  dime   piece 
stuck  on   with   wax.     Bow  both   forks.     Notice  beats. 
Change  half  dime  for  a  ten  cent  piece.     The  beats  be- 
come more  frequent.      Move  the  coin  higher  up  ;   the 
beats  become  still  more  frequent. 

45.  Determine  rate  of  loaded  fork  with  monochord 
(23),  knowing  that  of  unloaded.     Show  that  the  number 
of  beats  per  second  is  equal  to  the  difference  between  the 
numbers  of  vibrations  per  second  of  the  two  forks. 

46.  Increase  the  load  on  one  fork  till  harshness  or 
dissonance  ensues.     Again  compare  rates. 

47.  Longitudinal  Vibrations.     Solids. — Clamp  be- 
tween edges  of  wood  in  the  vice  (19)  in  the  middle  and 
horizontally  the  brass  tube  (25).     Rub  one  end  longitu- 
dinally with  wash-leather  (25)  covered  with  powdered 
rosin  (25).    Hang  a  pellet  of  wax  touching  the  other  end. 
Observe  how  it  is  thrown  off. 

48.  Let  two  glass  tubes  (25),  one  twice  as  long  as  the 
other,  be  held,  each  in  the  middle,  between  finger  and 
thumb,   and  let  one  end   of  each  be  rubbed  with  wet 
flannel  longitudinally.      The  longer  tube  produces  the 
lower  octave  of  the  shorter  one.     A  wave  of  compression 
has  to  travel  twice  as  far  from  end  to  end  and  back 
in  the  fc  rmer  as  in  the  latter  case,  and  therefore  takes 
twice  as  long ;  and  accordingly  in  the  same  time  it  re- 
appears and  hits  the  air  half  as  often.     Prove  this  by 
stretching  equally  two  pulley  wires  of  the  monochord  and 
moving  the  bridges  till  the  one  wire  is  in  unison  with  the 


Longitudinal  Vibrations.  147 

one  tube,  and  the  other  with  the  other  tube.     The  wires 
are  then  found  to  be  in  length  in  the  ratio  of  2  :  i. 

49.  Take  equal  lengths  of  deal  and  oak  rods  (25) ; 
hold  them  in  the  middle  and  rub  ends  with  rosined 
leathers.  The  note  from  the  oak  is  the  deepest.    Cut  (26) 
pieces    off   the  oak  rod  till  the  notes   are  in  unison. 
Measure  the  lengths.     The  lengths  are  in  the  proportion 
of  the  rates  of  progression  of  the  compression  wave  in  the 
respective  rods.     Because  the  compression  has  to  travel 
from  one  end  to  the  other,  and  back  again,  in  order  to 
beat  the  air  once  to  produce  one  sound  wave. 

50.  To  find  the  actual  rate,  tune,  by  cutting  one  of 
the  rods,  to  a  tuning-fork  of  known  rate  (No.  of  vibrations 
per  second).    This  is  best  done  by  augmenting  the  sound 
of  the  fork  by  holding  it  over  a  resonant  jar  or  cavity  (see 
below  55).     If  the  fork  gives  ;/  vibrations  to  and  fro  in 
one  second  and  the  rod  is  in  unison  with  it,  the  com- 
pression in  the  rod  must  travel  from  one  end  to  the  other 
and  back  (that  is,  twice  the  whole  length  of  the  rod)  n 
times  in  I  second.    Assuming  sound  to  travel  in  air  1,100 
feet  in  i  second,  it  travels  in  deal  about  16,000  feet  in  a 
second. 

51.  Hold  two  similar  wooden  rods,  one  in  the  middle, 
and  the  other  at  a  quarter  its  length  from  one  end.     Set 
both  in  longitudinal  vibration,  rubbing  the  shorter  end  of 
the  second,  octaves  will  be  produced.     The  second  rod 
will  have  a  node  at  a  quarter  its  length  from  the  further 
end. 

52.  Wrap  a  piece  of  thin  iron  wire  (23)  tightly  into  a 
close  spiral  round  the  brass  rod  (25).     Hang  the  spiral 
by  one  end,  and  hang  a  little  weight  at  the  other.     Note 
with  watch  the  number  of  jumps  the  wire  gives  in  a  few 
seconds   when   pulled   out.     Vary    its    length    and   the 
weight.     Compare  with   half  of  longitudinally  vibrating 
rod  clamped  in  the  middle. 

L  2 


148  Practical  Physics. 

53.  Fasten  rigidly  both  ends  of  the  wire  spiral  of  52. 
slightly  stretched  and  vertical.  Set  the  middle  moving 
up  and  down.  Also  damp  the  middle  and  pull  the 
centre  of  the  lower  half  gently  down  and  release  it.  The 
middle  forms  a  node.  Obtain  two  automatic  nodes  in  a 
similar  manner. 

5 |.  Tubes  open  and  closed  at  one  end. — Fasten  a 
piece  of  glass  tubing  (27)  about  18  inches  long  vertically. 
Fit  a  cork  into  the  bottom.  Through  the  cork  pass  a 
narrow  piece  of  glass  tubing.  Fasten  one  end  of  a  piece 
of  vulcanized  caoutchouc  tubing  about  three  feet  long  (i) 
to  this.  To  the  other  end  of  the  elastic  tubing  attach 
the  neck  of  a  funnel  (16).  Support  the  funnel  on  the 
filter  stand  (27).  Let  the  funnel  be  a  little  above  the  top 
of  the  tube.  Fill  both  with  water.  Sound  the  highest  ot 
the  three  forks  (7).  Hold  it  over  the  upright  tube,  de- 
press the  funnel  till  the  fork's  note  is  greatly  augmented. 
Lift  the  funnel  up  and  down,  and  fix  it  when  the  augmen- 
tation of  the  fork's  note  (resonance)  is  greatest.  Mark 
the  height  of  the  water  in  the  tube  exactly.  Cut  the  tube 
with  a  file  (26)  about  £  inch  below  mark.  Grind  it  down 
on  a  wet  hearth-stone  exactly  to  the  mark.  Cut  and 
grind  down  several  glass  tubes  of  this  same  length. 
Make  caps  for  the  tubes  by  cutting  round  discs  of 
card-board  as  large  as  the  outside  of  the  tubes,  these 
discs  can  be  stuck  on  to  the  ends  of  the  tubes  with 
beeswax. 

55.  Show  that  if  a  fork  resounds  with  a  tube  closed  at 
one  end  of  length  /,  it  will  resound  with  a  tube  open  at 
both  ends  of  length  2  /.     To  show  the  latter,  fasten  two 
tubes  together  by  an  inch  of  india-rubber  tubing  (27). 

56.  Show  that  if  a  fork  resounds  with  a  tube  of  length 
/  closed  at  one  end  it  will  resound  with  tubes  closed  at 
one  end  whose  lengths  are  3  /,  5  /,  7  /,  etc. 

57.  Show  that  if  a  fork  resounds  with  a  tube  open  at 


Vibrations  of  Air  in  Tubes.  149 

both  ends  of  length  /j  it  will  resound  with  tubes  open  at 
both  ends  whose  lengths  are  2  /„  3  /:,  4/,,  etc. 

58.  Show,  as  far  as  the  forks  at  disposal  will  allow, 
that  if  a  fork  resounds  with  a  tube  closed  at  one  end, 
those  forks  will  resound  with  the  same  tube  whose  notes 
are  the  next  harmonic  but  one,  the  next  but  three,  and  so 
on,  above  that  of  the  first  fork. 

59.  Show  that  if  a  fork  resounds  with  an  open  tube  all 
forks  will  do  so  whose  notes  are  higher  harmonics  of  the  first. 

60.  Admitting  that  for  all  notes  — 

wave  length  in  feet-    number  of  feet  traversed  in  i^ 
number  of  waves  generated  in  i  ' 

and  admitting  that  the  resonant  tube  closed  at  one  end  is 
\  the  wave  length  of  the  wave  system  of  the  lowest  note 
which  resounds  in  it,  deduce  (a)  the  rate  of  transmission 
of  sound  through  air,  knowing  the  number  of  vibrations 
of  a  fork  and  the  length  of  the  air  column  closed  at  one 
end  or  open  at  both,  which  resounds  with  it  ;  (b]  deduce 
the  wave-length,  assuming  the  rate  of  propagation  to  be 
1,100  feet  a  second,  and  knowing  the  pitch  of  the  fork  ; 
(c)  deduce  the  pitch  of  the  fork,  knowing  the  rate  of  pro- 
pagation and  the  length  of  the  resonant  column. 

61.  Heat  a  closed  tube,  which  resounds  with  a  given 
fork,  over  an  air  gas  flame.     Show  that  it  no  longer  re- 
sounds.    Invert  the  tube,  and  fill  it  with  coal  gas.     It  no 
longer  resounds.     Use  apparatus  in  54.    Get  the  tube 
when  containing  air  to  resound  to  a  fork  ;  fill  it  with  car- 
bonic acid  (17)  by  displacement  ;  show  that  the  column 
must  be  shoitened  to  resound  and  compare  lengths.  This 
should  verify  the  generalisation  that  when  d  is  the  density, 


62.  Effect  of  Relative  Motion  between  Origin  of 
Sound  and  Ear.  —  Fasten  a  whistle  (29)  in  one  end  of  a 


150  Practical  Physics. 

caoutchouc  tube  about  6  feet  long.  Sound  the  whistle 
by  blowing  into  the  other  end.  Whirl  the  tube  round 
while  continuing  to  blow,  and  notice  the  alteration  of 
pitch  at  different  pkces.  This  is  best  heard  at  a 
distance. 

63.  Singing  Flames.— Draw  out  a  piece   of  glass 
tubing  till  the  opening  at  the  end  is  about  as  wide  as  a 
pin.     Fasten  to  gas  pipe,  place  vertically,  and  light.    Re- 
duce the  flame  to  the  height  of  about  |  to  \  inch.    Clamp 
over  it  a  glass  tube  so  that  the  flame  is  about  a  quarter 
of  the  tube's  length  up  the  tube.     The  air  in  the  tube  will 
give  a  note.     Place  a  similar  jet  and  tube  side  by  side 
with  the  former  one.     Provide  each  tube  with  a  little 
sliding  tube  of  paper  so  as  to  be  able  to  alter  the  lengths, 
obtain  perfect  unison,  and  various  beats.     Show  that  the 
singing  of  the  flame  immediately  begins  if  the  voice  is 
pitched  to  the  note  which  the  flames  would  give.     Also 
start  by  a  consonant  tuning-fork. 

64.  Artificial  larynx.— Grind  off  the  top  of  a  glass 
tube  (27)  in  two  planes  at  an  angle  of  about  60°.    Stretch 
across  the  top  two  pieces  of  vulcanized  caoutchouc  (29) 
in  such  a  manner  that  there  is  a  slight  crack  between 
them,  bind  the  caoutchouc  on  to  the  tube  with  silk,  and 
blow  through. 


APPARATUS  AND  MATERIALS  FOR 
EXPERIMENTS  IN  SOUND  AND  WAVES. 

(1)  Three  similar  vulcanized  caoutchouc  tubes,  each 
about  £  inch  wide  and  12  feet  long.     One  filled  with 
sand  and  tied  up  at  the  ends.     A  piece  of  similar  tubing 
6  feet  long. 

(2)  A  long  narrow  wooden  trough  4  feet  x  6  inches  x 
6  inches  caulked  with  marine  glue,  and  painted  inside. 
Preferably  with  one  long  face  of  glass.     A  block  of  wood 
5f  inches  x  4  inches  x  4  inches,  with  handle  perpendicular 
from  middle  of  one  long  face.     Balls  of  wax  mixed  with 
iron  filings  so  as  just  to  float. 

(3)  Two  cylindrical  zinc  troughs  about  2  feet  and  18 
inches   diameter,   and    18   inches  deep.     A  rectangular 
trough  2  feet  x  i   foot  x  18  inches.     Silk  thread,  leaden 
bullets.     A  beaker  with  bottom  about  3  inches  diameter. 

(4)  A  box  about  18  inches  cube,  one  side  removed  and 
replaced  by  sailcloth  nailed  tight  on.     The  seams  of  the 
box  made  tight  by  paper  pasted  on  the  inside.  A  circular 
hole  in  the  side  of  the  box  opposite  to  the  canvas.     The 
hole  can  be  covered  by  a  plain  piece  of  cardboard.    Two 
holes,  side  by  side  on  one  side  of  the  box,  into  which  pass 
glass  tubes  bent  at  right  angles,  the  other  ends  of  which 
pass  through  corks  in  the  necks  of  two  flasks,  one  con- 
taining ammonia  and  the  other  hydrochloric  acid. 

(5)  Two  air  gas  burners  with  tubes. 

(6)  Fasten  a  tin  or  glass  tube,  £  inch  diameter,  to  the 
middle  of  a  circular  plate  of  tinplate  or  cardboard  about 
6  inches  in  diameter,  with  a  hole  in  the  middle  in  which 
the  tube  fits.     A  circular  piece  of  cardboard  somewhat 
less  than  the  disc. 


152  Practical  Physics. 

(7)  A  toy  air-ball,  the  larger  the  better.    Three  tuning- 
forks,  two  alike  and  one  an  octave  higher. 

(8)  A  glass  tube  about  |  inch  internal  diameter  and  50 
inches  long,  smoothly  and  as  flatly  as  possible  closed  at 
one  end.     The  tube  is  bent  into  two  parallel  limbs  at  a 
distance  of  about  10  inches  from  the  closed  end.     It  is 
fastened  to  an  upright  board  upon  which  are  ruled  hori- 
zontal lines  ^  inch  apart.     Enough  mercury  to  fill  the 
tube. 

(9)  A  stout  glass  tube  about  \  inch  internal  diameter 
and  6  inches  long,  closed  at  one  end  by  a  cork  which  is 
made  air-tight   by  sealing-wax.      A  cylindrical  wooden 
rod  just  passing  into  the  tube,  wrapped  round  at  one  end 
with  silk  thread,  till  it  just  fits  the  tube.    The  silk  is  oiled 
or  covered  with  glycerine.     A  piece  of  German  tinder. 
A  little  bisulphide  of  carbon. 

(10)  A  dozen  marbles  or  f  solitaire '  balls. 

(n)  A  deal  rod,  any  shape,  12  feet  long,  covered  with 
list,  hung  from  threads  or  clamped  horizontally.  A 
square  thin  deal  board,  not  cracked,  about  2  feet  square. 

(12)  A  glass  tube  about  18  inches  long  and  |  inch 
wide,  closed  at  one  end,  is  fastened  perpendicularly  by  a 
little  wax  to  the  board  (in  n),  which  is  supported  on  three 
corks.     The  tuning-fork  (7)  has    a  little  cone  of  cork 
fastened  to  one  face  of  one  prong  by  beeswax. 

(13)  Two  tinned  iron  tubes,  each  about  3  feet  long  and 
4  inches  diameter ;    the   end  of  one  fits  into  the  end 
of  the  other. 

(14)  A  pointed  deal  rod,  about  6  inches  long,  fastened 
to  a  square  light  deal  board  5  inches  square. 

(15)  A  hand  bell,  the  larger  the  better. 

(16)  A  glass  funnel  about  4  inches  in  diameter.  A  cork 
to  fit  its  neck.     A  clamp  or  support  for  the  funnel.     Car- 
bonate of  soda,  tartaric  acid. 

(17;  A  i  Ib.  flask,  fitted  with  a  cork  through  which 


Apparatus  and  Materials.  153 

pass  air-tight  (a)  a  straight  tube  reaching  to  the  bottom 
with  a  funnel  at  the  top,  (b)  a  tube  bent  at  right  angles, 
which  just  passes  through  the  cork.  Pieces  of  marble. 
Hydrochloric  acid. 

(18)  A    large   humming-top  with  a  smooth  but' on 
driven  into  its  peg.    Filled  with  sand  and  closed.    Resting 
upon  the  body  of  the  top  and  fastened  to  it  is  a  horizontal 
dis<:  of  thin  iron  plate,  having  200  or  300  teeth  in  its  cir- 
cumference.    Also  two  rings  of  holes  near  the  circum- 
ference.    One  ring  having  twice  as  many  holes  as  the 
other.    A  piece  of  quill  glass  tubing  bent  to  135°  at  one 
end. 

(19)  A  deal  rod,  about  12  feet  long,  i  inch  wide,  and  \ 
inch  thick.     The  ratio  of  width  to  thickness  should  be 
very  exact.     A  table  vice. 

(20)  A  round  knitting  needle.     Some  hollow  silvered 
glass  beads.     A  square  steel  rod,  about  8  inches  long, 
and  ^  inch  square.     A  rectangular  steel  rod,  about  8 
inches  long ;  one   side  i  inch,  the  other  ^  jnch.     The 
ratio  should  be  very  exact. 

(21)  A  straight  piece  of  clock  spring  about  I  foot  lonj 
is  softened  in  the  middle  in  the  flame  of  an   air-gas 
burner,  and  twisted  so  that  the  planes  of  the  two  parts 
are  at  right  angles  to  one  another. 

(22)  A  fiddle  bow.     Some  sheets  of  glass,  3  inches  x 
4  inches.     Some  oil  of  turpentine. 

(23)  Monochord,  etc.     An  inch  deal  board,  3  feet  long, 
9  inches  wide.    Two  pieces  of  wood,  6  inches  x  i  inch  x  i 
inch,  screwed  on  across  ends  to  form  supports.     Three 
long  wood  screws  driven  in  obliquely  (slanting  outwards) 
at  one  end  at  equal  distances.  At  the  other  end,  opposite 
one  screw,  is  a  pianoforte  peg,  at  an  angle  of  45.     Oppo- 
site the  other  two  screws  are  two  brass  pulleys  (window- 
blind  pulleys)  on  stems  which  are  driven  in  at  an  angle  of 
45°.     A  bridge,  that  is,  a  triangular  wedge  of  hard  wood, 


154  Practical  Physics. 

9  inches  long,  \  inch  wide  at  base,  and  as  high  as  the 
pulleys.  This  is  screwed  from  below  across  the  board 
about  3  inches  from  the  wooden  screws.  Three  other 
little  moveable  bridges  about  I  inch  long,  as  high  as  the 
pulleys,  are  provided.  A  variety  of  weights  and  hooks. 
A  pair  of  pliers.  Several  yards  of  iron  wire  (pianof  rte 
wire)  of  different  thicknesses.  Brass  wire,  seme  of  which 
has  the  sa(ne  thickness  as  some  c  f  the  iron  wire.  The 
ends  of  three  pieces  of  wire  are  twisted  into  loops  and 
passed  over  the  screw  heads.  One  of  the  other  ends  is 
passed  through  the  pianoforte  peg,  which  is  then  twisted 
round  by  the  pliers.  The  other  two  have  loops  twisted 
in  them,  and  passing  over  the  pulleys  carry  weights.  A 
sheet  of  paper  is  gummed  to  the  board  having  lines  at 
every  inch,  and  thinner  ones  at  every  TT5th  inch.  Mark 
with  o  the  line  beneath  the  pulleys  and  at  the  pianoforte 
peg. 

(24)  A  sheet  of  window  glass.     2  square  feet  of  patent 
plate  glass.     A  glazier's  diamond  or  steel  wheel-glass- 
cutter. 

(25)  Several  round  deal  and  oak  rods,  6  feet  long,  £ 
inch  diameter.     One  brass  rod  or  tube  £  inch  diameter, 
3  feet  long.     Glass  tube,  %  inch  diameter,  3  feet  long.     A 
square  foot  of  flannel.     A  piece  of  wash-leather.     Some 
powdered  rosin. 

(26)  Small  hand-saw.     Small  triangular  file. 

(27)  Twelve  feet  stout  glass  tubing,  f  inch  internal 
diameter.     A  few  inches  of  £  inch  tubing.     A  filter  stand 
and  a  retort  stand.     A  few  feet  of  vulcanized  caoutchouc 
tubing,  £  inch  internal  diameter. 

(28)  A  dog  whistle  without  the  pea. 

(29)  A  few  square  inches  of  thin  vulcanized  sheet 
caoutchouc. 


INDEX. 


The  nuvtbers  refer  to  the  paragraphs. 


ABS 

ABSORPTION   (of  gases    by  li- 
quids), 36,  37 
Approach  caused  by  vibration,  109 

BAROMETER  siphon,  115 

Beats,  103,  104 

Bell,  92 

Breath  pictures,  42 

Bubbles,  14-18 

CAPILLARITY,  24-29 

Closed  and  open  pipes,  96-98 
Cohesion  of  gases  (viscosity),  19 

liquids,  8-18 

liquids  affected  by  adhesion  to 

solids,  24-29 

solids,  1-7 

solids  affected  by  adhesion  to 

liquids,  30-32 

Colloids,  vapour  tension  of,  55 
Condensation    of   gases    on  solids, 

38-42 
Conversion  of  sound  into  notes,  80 

DENSITY,  60-73 

Detection  of  sound,  81 

Dialysis,  57,  58       . 

Diffusion  of  gases  into  gases,  43-46 

into  liquids,  36-37 

• into  solids,  38-41 

liquids  into  gases,  evaporation, 

49 

liquids  into  liquids,  33-35 

liquids  into  solids,  56 

Drop  size,  12,  13 

EFFUSION  of  gases,  47 
Elasticity  of  gases,  21-23 


PHON 

Elasticity  of  solids,  4-7 
Etching  on  glass,  114 
Evaporation  of  liquids  into 
49 

GAS-  WAVE,  96-99 

Glass  etching,  114 

Glass  working  (hints  on),  113 

HARDNESS  of  solids,  i 
INTERFERENCE,  103-106 
JETS  (Liquid),  10 


LIQUID  waves,  76-78  ' 
Longitudinal  vibrations  of  liquids, 

100 
Longitudinal    vibrations    of   solids, 

100-112 

MOTION  (effect  of  on  sound),  108 
Musical  scale,  90 

NODES,  in  pipes.  98 
---  plates,  93-95 
--  rods,  91 

--  strings.  86-88 
Notes  derived  from  sound,  80 

OCCLUSION,  40,  41 

Open  and  closed  pipes,  96-98 

Origins  of  sound  waves,  84  et  sef.t 

89  et  seq. 
Osmose,  56 

PARCHMENT  paper,  il* 
Phonograph,  no 


IS6 


Index. 


REFL 

REFLEXION  of  sound,  82 
Reflexion  of  water-wave,  77-78 
Refraction  of  sound,  83 
Resonance,  99 
Rods,  transverse  vibrations  of,  84-85 

SENSITIVE  flame,  81 

Singing  flame,  106 

Sinuosities,  107 

Siphon  barometer,  115 

Solids,    longitudinal    vibrations  of, 

ICX>-I02 

Solution  (of  solids  in  liquids),  30-32 
Specific  gravity,  60-73 

of  liquids,  67-70 

of  solids,  62-66,  71-73 

Stationary  water-waves,  77-78 
Strings    (transverse    vibrations   of), 

86-89 
Sympathy,  108 


WAV 

TENACITY,  2-3 

Thunder,  92 

Torsion,  4-6 

Transpiration,  59 

Transverse  vibrations  of  rods,  84,  85 

strings,  86-89 

VAPOUR  tension,  51-55 

Vernier,  the,  in 

Vibrating  strings  as  source  of  sound, 

89 

Vibration  of  rods  (transverse),  84,  85 
Volume  hardness,  20-23 
Vortex  rings,  74 

WATER-WAVES,  76-78  m 
Waves  governed  by  elasticity,  79 

gravity,  76-78 

—  in  general,  75 
-  liquid,  76-78 


UNIVERSITY  OF 


\ 


